NR Polar imports

openair1/PHY/CODING/TESTBENCH/polartest.c

+#include <math.h>
+#include <stdio.h>
+#include <stdint.h>
+#include <stdlib.h>
+#include <string.h>
+#include <sys/stat.h>
+#include <time.h>
+
+#include "PHY/CODING/nrPolar_tools/nr_polar_defs.h"
+#include "PHY/CODING/nrPolar_tools/nr_polar_pbch_defs.h"
+#include "SIMULATION/TOOLS/defs.h"
+
+int main(int argc, char *argv[]) {
+
+	//Initiate timing. (Results depend on CPU Frequency. Therefore, might change due to performance variances during simulation.)
+	time_stats_t timeEncoder,timeDecoder;
+	opp_enabled=1;
+	cpu_freq_GHz = get_cpu_freq_GHz();
+	reset_meas(&timeEncoder);
+	reset_meas(&timeDecoder);
+
+	randominit(0);
+	//Default simulation values (Aim for iterations = 1000000.)
+	int itr, iterations = 1000, arguments, polarMessageType = 1; //0=DCI, 1=PBCH, 2=UCI
+	double SNRstart = -20.0, SNRstop = 20.0, SNRinc= 0.5; //dB
+
+	double SNR, SNR_lin;
+	int16_t nBitError = 0; // -1 = Decoding failed (All list entries have failed the CRC checks).
+	int8_t decoderState=0, blockErrorState=0; //0 = Success, -1 = Decoding failed, 1 = Block Error.
+	uint16_t testLength, coderLength, blockErrorCumulative=0, bitErrorCumulative=0;
+	double timeEncoderCumulative = 0, timeDecoderCumulative = 0;
+
+	uint8_t decoderListSize = 8, pathMetricAppr = 0; //0 --> eq. (8a) and (11b), 1 --> eq. (9) and (12)
+
+	while ((arguments = getopt (argc, argv, "s:d:f:m:i:l:a:")) != -1)
+	switch (arguments)
+	{
+		case 's':
+			SNRstart = atof(optarg);
+			printf("SNRstart = %f\n", SNRstart);
+			break;
+
+		case 'd':
+			SNRinc = atof(optarg);
+			break;
+
+		case 'f':
+			SNRstop = atof(optarg);
+			break;
+
+		case 'm':
+			polarMessageType = atoi(optarg);
+			break;
+
+		case 'i':
+			iterations = atoi(optarg);
+			break;
+
+		case 'l':
+			decoderListSize = (uint8_t) atoi(optarg);
+			break;
+
+		case 'a':
+			pathMetricAppr = (uint8_t) atoi(optarg);
+			break;
+
+		default:
+			perror("[polartest.c] Problem at argument parsing with getopt");
+			abort ();
+	}
+
+	if (polarMessageType == 0) { //DCI
+		//testLength = ;
+		//coderLength = ;
+	} else if (polarMessageType == 1) { //PBCH
+		testLength = NR_POLAR_PBCH_PAYLOAD_BITS;
+		coderLength = NR_POLAR_PBCH_E;
+	} else if (polarMessageType == 2) { //UCI
+		//testLength = ;
+		//coderLength = ;
+	}
+
+	//Logging
+	time_t currentTime;
+	time (&currentTime);
+	char fileName[512], currentTimeInfo[25];
+
+	sprintf(fileName,"./polartestResults/_ListSize_%d_pmAppr_%d_Payload_%d_Itr_%d",decoderListSize,pathMetricAppr,testLength,iterations);
+	strftime(currentTimeInfo, 25, "_%Y-%m-%d-%H-%M-%S.csv", localtime(&currentTime));
+	strcat(fileName,currentTimeInfo);
+
+	//Create "./polartestResults" folder if it doesn't already exist.
+	struct stat folder = {0};
+	if (stat("./polartestResults", &folder) == -1) mkdir("./polartestResults", S_IRWXU | S_IRWXO);
+
+    FILE* logFile;
+    logFile = fopen(fileName, "w");
+    if (logFile==NULL) {
+        fprintf(stderr,"[polartest.c] Problem creating file %s with fopen\n",fileName);
+        exit(-1);
+      }
+    fprintf(logFile,",SNR,nBitError,blockErrorState,t_encoder[us],t_decoder[us]\n");
+
+	uint8_t *testInput = malloc(sizeof(uint8_t) * testLength); //generate randomly
+	uint8_t *encoderOutput = malloc(sizeof(uint8_t) * coderLength);
+	double *modulatedInput = malloc (sizeof(double) * coderLength); //channel input
+
+	double *channelOutput  = malloc (sizeof(double) * coderLength); //add noise
+	uint8_t *estimatedOutput = malloc(sizeof(uint8_t) * testLength); //decoder output
+
+	t_nrPolar_params nrPolar_params;
+	nr_polar_init(&nrPolar_params, polarMessageType);
+
+	// We assume no a priori knowledge available about the payload.
+	double aPrioriArray[nrPolar_params.payloadBits];
+	for (int i=0; i<nrPolar_params.payloadBits; i++) aPrioriArray[i] = NAN;
+
+	for (SNR = SNRstart; SNR <= SNRstop; SNR += SNRinc) {
+		SNR_lin = pow(10, SNR/10);
+		for (itr = 1; itr <= iterations; itr++) {
+
+		for(int i=0; i<testLength; i++) testInput[i]=(uint8_t) (rand() % 2);
+
+		start_meas(&timeEncoder);
+		polar_encoder(testInput, encoderOutput, &nrPolar_params);
+		stop_meas(&timeEncoder);
+
+		//BPSK modulation
+		for(int i=0; i<coderLength; i++) {
+			if (encoderOutput[i] == 0)
+				modulatedInput[i]=1/sqrt(2);
+			else
+				modulatedInput[i]=(-1)/sqrt(2);
+
+			channelOutput[i] = modulatedInput[i] + (gaussdouble(0.0,1.0) * (1/sqrt(2*SNR_lin)));
+		}
+
+
+		start_meas(&timeDecoder);
+		decoderState = polar_decoder(channelOutput, estimatedOutput, &nrPolar_params, decoderListSize, aPrioriArray, pathMetricAppr);
+		stop_meas(&timeDecoder);
+
+		//calculate errors
+		if (decoderState==-1) {
+			blockErrorState=-1;
+			nBitError=-1;
+		} else {
+			for(int i=0; i<testLength; i++){
+				if (estimatedOutput[i]!=testInput[i]) nBitError++;
+			}
+			if (nBitError>0) blockErrorState=1;
+		}
+
+		//Iteration times are in microseconds.
+		timeEncoderCumulative+=(timeEncoder.diff_now/(cpu_freq_GHz*1000.0));
+		timeDecoderCumulative+=(timeDecoder.diff_now/(cpu_freq_GHz*1000.0));
+		fprintf(logFile,",%f,%d,%d,%f,%f\n", SNR, nBitError, blockErrorState,
+				(timeEncoder.diff_now/(cpu_freq_GHz*1000.0)), (timeDecoder.diff_now/(cpu_freq_GHz*1000.0)));
+
+		if (nBitError<0) {
+			blockErrorCumulative++;
+			bitErrorCumulative+=testLength;
+		} else {
+			blockErrorCumulative+=blockErrorState;
+			bitErrorCumulative+=nBitError;
+		}
+
+		decoderState=0;
+		nBitError=0;
+		blockErrorState=0;
+
+		}
+		//Calculate error statistics for the SNR.
+		printf("[ListSize=%d, Appr=%d] SNR=%+8.3f, BLER=%9.6f, BER=%12.9f, t_Encoder=%9.3fus, t_Decoder=%9.3fus\n",
+				decoderListSize, pathMetricAppr, SNR, ((double)blockErrorCumulative/iterations),
+				((double)bitErrorCumulative / (iterations*testLength)),
+				(timeEncoderCumulative/iterations),timeDecoderCumulative/iterations);
+
+		blockErrorCumulative = 0; bitErrorCumulative = 0;
+		timeEncoderCumulative = 0; timeDecoderCumulative = 0;
+	}
+
+	print_meas(&timeEncoder,"polar_encoder",NULL,NULL);
+	print_meas(&timeDecoder,"polar_decoder",NULL,NULL);
+
+	fclose(logFile);
+	free(testInput);
+	free(encoderOutput);
+	free(modulatedInput);
+	free(channelOutput);
+	free(estimatedOutput);
+
+	return (0);
+}

openair1/PHY/CODING/nrPolar_init.c

+#include "nrPolar_tools/nr_polar_defs.h"
+#include "nrPolar_tools/nr_polar_pbch_defs.h"
+
+void nr_polar_init(t_nrPolar_params* polarParams, int messageType) {
+
+	if (messageType == 0) { //DCI
+
+	} else if (messageType == 1) { //PBCH
+		polarParams->n_max = NR_POLAR_PBCH_N_MAX;
+		polarParams->i_il = NR_POLAR_PBCH_I_IL;
+		polarParams->n_pc = NR_POLAR_PBCH_N_PC;
+		polarParams->n_pc_wm = NR_POLAR_PBCH_N_PC_WM;
+		polarParams->i_bil = NR_POLAR_PBCH_I_BIL;
+		polarParams->payloadBits = NR_POLAR_PBCH_PAYLOAD_BITS;
+		polarParams->encoderLength = NR_POLAR_PBCH_E;
+		polarParams->crcParityBits = NR_POLAR_PBCH_CRC_PARITY_BITS;
+		polarParams->crcCorrectionBits = NR_POLAR_PBCH_CRC_ERROR_CORRECTION_BITS;
+
+		polarParams->K = polarParams->payloadBits + polarParams->crcParityBits; // Number of bits to encode.
+		polarParams->N = nr_polar_output_length(polarParams->K, polarParams->encoderLength, polarParams->n_max);
+		polarParams->n = log2(polarParams->N);
+
+		polarParams->crc_generator_matrix=crc24c_generator_matrix(polarParams->payloadBits);
+		polarParams->G_N = nr_polar_kronecker_power_matrices(polarParams->n);
+	} else if (messageType == 2) { //UCI
+
+	}
+
+	polarParams->Q_0_Nminus1 = nr_polar_sequence_pattern(polarParams->n);
+
+	polarParams->interleaving_pattern = (uint16_t *)malloc(sizeof(uint16_t) * polarParams->K);
+	nr_polar_interleaving_pattern(polarParams->K, polarParams->i_il, polarParams->interleaving_pattern);
+
+	polarParams->rate_matching_pattern = (uint16_t *)malloc(sizeof(uint16_t) * polarParams->encoderLength);
+	uint16_t *J = malloc(sizeof(uint16_t) * polarParams->N);
+	nr_polar_rate_matching_pattern(polarParams->rate_matching_pattern, J, nr_polar_subblock_interleaver_pattern,
+			polarParams->K, polarParams->N, polarParams->encoderLength);
+
+
+	polarParams->information_bit_pattern = malloc(sizeof(uint8_t) * polarParams->N);
+	polarParams->Q_I_N = malloc(sizeof(int16_t) * (polarParams->K + polarParams->n_pc));
+	polarParams->Q_F_N = malloc(sizeof(int16_t) * (polarParams->N+1)); // Last element shows the final array index assigned a value.
+	polarParams->Q_PC_N = malloc(sizeof(int16_t) * (polarParams->n_pc));
+	for (int i=0; i<=polarParams->N; i++) polarParams->Q_F_N[i] = -1; // Empty array.
+	nr_polar_info_bit_pattern(polarParams->information_bit_pattern,
+			polarParams->Q_I_N, polarParams->Q_F_N, J, polarParams->Q_0_Nminus1,
+			polarParams->K, polarParams->N, polarParams->encoderLength, polarParams->n_pc);
+
+	polarParams->channel_interleaver_pattern = malloc(sizeof(uint16_t) * polarParams->encoderLength);
+	nr_polar_channel_interleaver_pattern(polarParams->channel_interleaver_pattern,
+			polarParams->i_bil, polarParams->encoderLength);
+
+	free(J);
+}

openair1/PHY/CODING/nrPolar_tools/get_3GPP_info_bit_pattern.c

+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+#include <stdint.h>
+
+void get_3GPP_info_bit_pattern(uint16_t K, uint16_t n_PC, uint16_t Q_N_length, uint8_t E_r, uint8_t* P, uint16_t* Q_N, uint8_t** info_bit_pattern)
+{
+//   GET_3GPP_INFO_BIT_PATTERN Obtain the 3GPP information bit pattern,
+//   according to Section 5.4.1.1 of 3GPP TS 38.212
+//
+//   I should be an integer scalar. It specifies the number of bits in the
+//   information, CRC and PC bit sequence. It should be no greater than N or E.
+//
+//   Q_N should be a row vector comprising N number of unique integers in the
+//   range 1 to N. Each successive element of Q_N provides the index of the
+//   next most reliable input to the polar encoder kernal, where the first
+//   element of Q_N gives the index of the least reliable bit and the last
+//   element gives the index of the most reliable bit.
+//
+//   rate_matching_pattern should be a vector comprising E_r number of
+//   integers, each having a value in the range 1 to N. Each integer
+//   identifies which one of the N outputs from the polar encoder kernal
+//   provides the corresponding bit in the encoded bit sequence e.
+//
+//   mode should have the value 'repetition', 'puncturing' or 'shortening'.
+//   This specifies how the rate matching has been achieved. 'repetition'
+//   indicates that some outputs of the polar encoder kernal are repeated in
+//   the encoded bit sequence two or more times. 'puncturing' and
+//   'shortening' indicate that some outputs of the polar encoder kernal
+//   have been excluded from the encoded bit sequence. In the case of
+//   'puncturing' these excluded bits could have values of 0 or 1. In the
+//   case of 'shortening' these excluded bits are guaranteed to have values
+//   of 0.
+//
+//   info_bit_pattern will be a vector comprising N number of logical
+//   elements, each having the value true or false. The number of elements
+//   in info_bit_pattern having the value true will be I. These elements
+//   having the value true identify the positions of the information and
+//   CRC bits within the input to the polar encoder kernal. The
+//   information bit arrangement can be achieved according to
+//   u(info_bit_pattern) = a.
+
+int I=K+n_PC;
+
+        if (I > Q_N_length) //I=K+n_PC
+        {
+            fprintf(stderr, "I=K+n_PC should be no greater than N.");
+            exit(-1);
+        }
+        if (I > E_r)
+        {
+            fprintf(stderr, "I=K+n_PC should be no greater than E.");
+            exit(-1);
+        }
+
+        //This is how the rate matching is described in TS 38.212
+        int J[Q_N_length];
+        int i,j;
+        for (j=0; j<Q_N_length; j++)
+        {
+            i=floor(32*(double)j/Q_N_length);
+            J[j] = P[i]*(Q_N_length/32)+(j%(Q_N_length/32));
+        }
+
+        //Q_Ftmp_N = [];
+        int Q_Ftmp_N_length= Q_N_length-E_r;
+        if (E_r < Q_N_length)
+        {
+            if ((double)(I)/E_r <= (double)7/16) // puncturing
+            {
+                //Q_Ftmp_N_length = Q_Ftmp_N_length + N-E;
+                if (E_r >= (double)3*Q_N_length/4)
+                {
+                    //Q_Ftmp_N = [Q_Ftmp_N,0:ceil(3*N/4-E/2)-1];
+                    Q_Ftmp_N_length = Q_Ftmp_N_length + ceil(3*Q_N_length/4-(double)E_r/2);
+                } else
+                {
+                    //Q_Ftmp_N = [Q_Ftmp_N,0:ceil(9*N/16-E/4)-1];
+                    Q_Ftmp_N_length = Q_Ftmp_N_length + ceil(9*Q_N_length/16-(double)E_r/4);
+                }
+            }
+        }
+
+        int* Q_Ftmp_N = (int *)malloc(sizeof(int)*Q_Ftmp_N_length);
+        if (Q_Ftmp_N == NULL)
+        {
+            fprintf(stderr, "malloc failed\n");
+            exit(-1);
+        }
+        if (E_r < Q_N_length)
+        {
+            if ((double)I/E_r <= 7/16) // puncturing
+            {
+                for (j=0; j<Q_N_length-E_r; j++)
+                {
+                    Q_Ftmp_N[j] = J[j];
+                }
+
+                if (E_r >= 3*Q_N_length/4)
+                {
+                    for (j=0; j<ceil(3*Q_N_length/4-(double)E_r/2); j++)
+                    {
+                        Q_Ftmp_N[Q_N_length-E_r+1+j] = j;
+                    }
+                } else
+                {
+                    for (j=0; j<ceil(9*Q_N_length/16-(double)E_r/4); j++)
+                    {
+                        Q_Ftmp_N[Q_N_length-E_r+1+j] = j;
+                    }
+                }
+            } else // shortening
+            {
+                for (j=E_r; j<Q_N_length; j++)
+                {
+                    Q_Ftmp_N[j-E_r] = J[j];
+                }
+
+            }
+        }
+
+        //Q_Itmp_N = setdiff(Q_N-1,Q_Ftmp_N,'stable'); // -1 because TS 38.212 assumes that indices start at 0, not 1 like in Matlab
+        int Q_Itmp_N_length = Q_N_length;
+        int Q_Itmp_N_common[Q_N_length];
+
+        for(i=0; i<Q_N_length; i++)
+        {
+            Q_Itmp_N_common[i]=0; //1 if in common, otherwise 0
+
+            for (j=0; j<Q_Ftmp_N_length; j++)
+            {
+                if((int)Q_N[i]==Q_Ftmp_N[j])
+                {
+                    Q_Itmp_N_common[i]=1;
+                    Q_Itmp_N_length--;
+                    break;
+                }
+            }
+        }
+
+        free(Q_Ftmp_N);
+
+        if (Q_Itmp_N_length < I)
+        {
+            fprintf(stderr, "Too many pre-frozen bits.");
+            exit(-1);
+        }
+
+        int* Q_Itmp_N = (int *)malloc(sizeof(int)*Q_Itmp_N_length);
+        if (Q_Itmp_N == NULL)
+        {
+            fprintf(stderr, "malloc failed\n");
+            exit(-1);
+        }
+        j=0;
+        for(i=0; i<Q_N_length; i++)
+        {
+            if(!Q_Itmp_N_common[i]) //if not commonc
+            {
+                Q_Itmp_N[j]=(int)Q_N[i];
+                j++;
+            }
+        }
+
+        int* Q_I_N = (int *)malloc(sizeof(int)*(I));
+        if (Q_I_N == NULL)
+        {
+            fprintf(stderr, "malloc failed\n");
+            exit(-1);
+        }
+        //Q_I_N=Q_Itmp_N(end-I+1:end);
+        for (j=Q_Itmp_N_length-(I); j<Q_Itmp_N_length; j++)
+        {
+            Q_I_N[j-(Q_Itmp_N_length-(I))]=Q_Itmp_N[j];
+        }
+
+        free(Q_Itmp_N);
+
+        //info_bit_pattern(Q_I_N+1) = true;
+        *info_bit_pattern = (uint8_t *)malloc(sizeof(uint8_t)*Q_N_length);
+        if (*info_bit_pattern == NULL)
+        {
+            fprintf(stderr, "malloc failed\n");
+            exit(-1);
+        }
+        for(j=0; j<Q_N_length; j++)
+        {
+            (*info_bit_pattern)[j]=0;
+            for(i=0; i<I; i++)
+            {
+                if(Q_I_N[i]==j)
+                {
+                    (*info_bit_pattern)[j]=1;
+                    break;
+                }
+            }
+        }
+
+        free(Q_I_N);
+}

openair1/PHY/CODING/nrPolar_tools/get_PC_bit_pattern.c

+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+#include <stdint.h>
+
+void get_PC_bit_pattern(uint16_t Q_N_length, uint16_t n_PC, uint8_t n_PC_wm, uint16_t* Q_N, uint8_t* info_bit_pattern, uint8_t** PC_bit_pattern)
+{
+//   GET_PC_BIT_PATTERN Obtain the Parity Check (PC) bit pattern,
+//   according to Section 5.3.1.2 of 3GPP TS 38.212
+//
+//   info_bit_pattern should be a vector comprising N number of logical
+//   elements, each having the value true or false. The number of elements
+//   in info_bit_pattern having the value true should be I, where
+//   I = A+P+n_PC. These elements having the value true identify the
+//   positions of the information, CRC and PC bits within the input to the
+//   polar encoder kernal.
+//
+//   Q_N should be a row vector comprising N number of unique integers in the
+//   range 1 to N. Each successive element of Q_N provides the index of the
+//   next most reliable input to the polar encoder kernal, where the first
+//   element of Q_N gives the index of the least reliable bit and the last
+//   element gives the index of the most reliable bit.
+//
+//   n_PC should be an integer scalar. It specifies the number of PC bits to
+//   use, where n_PC should be no greater than I.
+//
+//   n_PC_wm should be an integer scalar. It specifies the number of PC bits
+//   that occupy some of the most reliable positions at the input to the
+//   polar encoder kernal. The remaining n_PC-n_PC_wm PC bits occupy some of
+//   the least reliable positions at the input to the polar encoder kernal.
+//   n_PC_wm should be no greater than n_PC.
+//
+//   PC_bit_pattern will be a vector comprising N number of logical
+//   elements, each having the value true or false. The number of elements
+//   in PC_bit_pattern having the value true will be n_PC.
+//   These elements having the value true identify the positions of the
+//   PC bits within the input to the polar encoder kernal.
+
+        //N = length(info_bit_pattern); -> Q_N_length
+        //I = sum(info_bit_pattern);
+        int totInfoBit =0;
+        int j,i;
+        for (j=0; j<Q_N_length; j++)
+        {
+            if(info_bit_pattern[j])
+                totInfoBit++;
+        }
+
+        if (n_PC > totInfoBit)
+        {
+            fprintf(stderr, "n_PC should be no greater than totInfoBit.");
+            exit(-1);
+        }
+
+        if (n_PC_wm > n_PC)
+        {
+            fprintf(stderr, "n_PC_wm should be no greater than n_PC.");
+            exit(-1);
+        }
+        //Q_I = 1:N;
+        int* Q_I = (int*) malloc(sizeof(int)*Q_N_length);
+        if (Q_I == NULL)
+        {
+            fprintf(stderr, "malloc failed\n");
+            exit(-1);
+        }
+        for (j=0; j<Q_N_length; j++)
+        {
+            Q_I[j]=j+1;
+        }
+
+        //Q_N_I = intersect(Q_N, Q_I(info_bit_pattern), 'stable');
+        int Q_N_I_length=0;
+        int* Q_N_common = (int*) malloc(sizeof(int)*Q_N_length);
+        if (Q_N_common == NULL)
+        {
+            fprintf(stderr, "malloc failed\n");
+            exit(-1);
+        }
+
+        for (j=0; j<Q_N_length; j++) //init
+        {
+            Q_N_common[j]=0;
+        }
+
+        for (j=0; j<Q_N_length; j++) //look in Q_I
+        {
+            if(info_bit_pattern[j])
+            {
+                //Q_I(info_bit_pattern)
+                for (i=0; i<Q_N_length; i++) //look in Q_N
+                {
+                    if(Q_N[i]+1==Q_I[j])
+                    {
+                        Q_N_common[i]=1;
+                        Q_N_I_length++;
+                        break;
+                    }
+                }
+            }
+        }
+        free(Q_I);
+
+        int* Q_N_I =  (int*) malloc(sizeof(int)*Q_N_I_length);
+        if (Q_N_I == NULL)
+        {
+            fprintf(stderr, "malloc failed\n");
+            exit(-1);
+        }
+        i=0;
+        for(j=0; j<Q_N_length; j++)
+        {
+            if(Q_N_common[j])
+            {
+                Q_N_I[i]=Q_N[j]+1;
+                i++;
+            }
+        }
+
+        free(Q_N_common);
+
+        //int G_N = get_G_N(N);
+        //int w_g = sum(G_N,2);
+        //useless, I do this
+        int* w_g = (int*) malloc(sizeof(int)*Q_N_length);
+        if (w_g == NULL)
+        {
+            fprintf(stderr, "malloc failed\n");
+            exit(-1);
+        }
+        w_g[0]=1;
+        w_g[1]=2;
+        int counter=2;
+        int n = log2(Q_N_length);
+
+        for(i=0; i<n-1; i++) //n=log2(N)
+        {
+            for(j=0; j<counter; j++)
+            {
+                w_g[counter+j]=w_g[j]*2;
+            }
+            counter = counter*2;
+        }
+
+        //Q_tilde_N_I = Q_N_I(n_PC+1:end); % This is what it says in TS 38.212
+        int* Q_tilde_N_I = (int*) malloc(sizeof(int)*(Q_N_I_length-n_PC));
+        if (Q_tilde_N_I == NULL)
+        {
+            fprintf(stderr, "malloc failed\n");
+            exit(-1);
+        }
+        int* Q_tilde_N_I_flip = (int*) malloc(sizeof(int)*(Q_N_I_length-n_PC));
+        if (Q_tilde_N_I_flip == NULL)
+        {
+            fprintf(stderr, "malloc failed\n");
+            exit(-1);
+        }
+        for (i=0; i<Q_N_I_length-n_PC; i++)
+        {
+            Q_tilde_N_I[i]=Q_N_I[n_PC+i];
+            //Q_tilde_N_I_flip = fliplr(Q_tilde_N_I);
+            Q_tilde_N_I_flip[Q_N_I_length-n_PC-i-1] = Q_tilde_N_I[i];
+        }
+        //%Q_tilde_N_I = Q_N_I(n_PC-n_PC_wm+1:end); % I think that this would be slightly more elegant
+
+        //[w_g_sorted, indices] = sort(w_g(Q_tilde_N_I_flip));
+        int* w_g_sorted =  (int*) malloc(sizeof(int)*(Q_N_I_length-n_PC));
+        if (w_g_sorted == NULL)
+        {
+            fprintf(stderr, "malloc failed\n");
+            exit(-1);
+        }
+        int* indices =  (int*) malloc(sizeof(int)*(Q_N_I_length-n_PC));
+        if (indices == NULL)
+        {
+            fprintf(stderr, "malloc failed\n");
+            exit(-1);
+        }
+        for (i=0; i<Q_N_I_length-n_PC; i++)
+        {
+            w_g_sorted[i]=w_g[Q_tilde_N_I_flip[i]-1]; // w_g(Q_tilde_N_I_flip), yet to sort
+            indices[i] = i;
+        }
+        free(Q_tilde_N_I);
+        free(w_g);
+
+        //bubble sort
+        int tempToSwap=0;
+        for (i = 0; i < (Q_N_I_length-n_PC)-1; i++)
+        {
+            for (j = 0; j < (Q_N_I_length-n_PC)-i-1; j++)
+            {
+                 if (w_g_sorted[j] > w_g_sorted[j+1]) //then swap
+                 {
+                     tempToSwap = w_g_sorted[j];
+                     w_g_sorted[j] = w_g_sorted[j+1];
+                     w_g_sorted[j+1] = tempToSwap;
+
+                     tempToSwap = indices[j];
+                     indices[j] = indices[j+1];
+                     indices[j+1] = tempToSwap;
+                 }
+            }
+        }
+        free(w_g_sorted);
+
+        //Q_N_PC = [Q_N_I(1:n_PC-n_PC_wm), Q_tilde_N_I_flip(indices(1:n_PC_wm))];
+        int* Q_N_PC = (int*) malloc(sizeof(int)*(n_PC));
+        if (Q_N_PC == NULL)
+        {
+            fprintf(stderr, "malloc failed\n");
+            exit(-1);
+        }
+
+        for (i=0; i<n_PC-n_PC_wm; i++)
+        {
+            Q_N_PC[i]=Q_N_I[i]; //Q_N_PC = [Q_N_I(1:n_PC-n_PC_wm), ...
+        }
+        free(Q_N_I);
+
+        for (i=0; i<n_PC_wm; i++)
+        {
+            Q_N_PC[n_PC-n_PC_wm+i] = Q_tilde_N_I_flip[indices[i]];//... Q_tilde_N_I_flip(indices(1:n_PC_wm))];
+        }
+        free(Q_tilde_N_I_flip);
+        free(indices);
+
+        //PC_bit_pattern = false(1,N);
+        //PC_bit_pattern(Q_N_PC) = true;
+        *PC_bit_pattern =  (uint8_t*) malloc(sizeof(uint8_t)*(Q_N_length));
+        if (*PC_bit_pattern == NULL)
+        {
+            fprintf(stderr, "malloc failed\n");
+            exit(-1);
+        }
+
+        for (i=0; i<Q_N_length; i++)
+        {
+            (*PC_bit_pattern)[i]=0;
+            for (j=0; j<n_PC; j++)
+            {
+                if (Q_N_PC[j]-1==i)
+                {
+                    (*PC_bit_pattern)[i]=1;
+                    break;
+                }
+            }
+        }
+
+        //free(Q_I);
+        //free(Q_N_common);
+        //free(Q_N_I);
+        //free(w_g);
+        //free(Q_tilde_N_I);
+        //free(Q_tilde_N_I_flip);
+        //free(w_g_sorted);
+        //free(indices);
+        free(Q_N_PC);
+}

openair1/PHY/CODING/nrPolar_tools/get_crc_generator_matrix.c

+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+#include <stdint.h>
+
+void get_crc_generator_matrix(uint8_t A, uint8_t P, uint8_t* crc_polynomial_pattern, uint8_t*** G_P)
+{
+//   GET_CRC_GENERATOR_MATRIX Obtain a Cyclic Redudancy Check (CRC) generator
+//   matrix.
+//
+//   A should be an integer scalar. It specifies the number of bits in the
+//   information bit sequence.
+//
+//   crc_polynomial_pattern should be a binary row vector comprising P+1
+//   number of bits, each having the value 0 or 1. These bits parameterise a
+//   Cyclic Redundancy Check (CRC) comprising P bits. Each bit provides the
+//   coefficient of the corresponding element in the CRC generator
+//   polynomial. From left to right, the bits provide the coefficients for
+//   the elements D^P, D^P-1, D^P-2, ..., D^2, D, 1.
+//
+//   G_P will be a K by P binary matrix. The CRC bits can be generated
+//   according to mod(a*G_P,2).
+
+        *G_P = (uint8_t **)malloc(A * sizeof(uint8_t *));
+        if (*G_P == NULL)
+        {
+            fprintf(stderr, "malloc failed\n");
+            exit(-1);
+        }
+        int i,j;
+        for (i=0; i<A; i++)
+        {
+            (*G_P)[i] = (uint8_t *)malloc(P * sizeof(uint8_t));
+            if ((*G_P)[i] == NULL)
+            {
+                fprintf(stderr, "malloc failed\n");
+                exit(-1);
+            }
+        }
+
+        if(A>0)
+        {
+            //G_P(end,:) = crc_polynomial_pattern(2:end);
+            for(i=0; i<P; i++)
+            {
+                (*G_P)[A-1][i] = crc_polynomial_pattern[i+1];
+            }
+
+            //for k = A-1:-1:1
+            //    G_P(k,:) = xor([G_P(k+1,2:end),0],G_P(k+1,1)*crc_polynomial_pattern(2:end));
+            //end
+            for(j=A-2; j>-1; j--)
+            {
+                for(i=0; i<P; i++)
+                {
+                    (*G_P)[j][i]=0; //init with zeros
+                }
+
+                for(i=1; i<P; i++)
+                {
+                    if( (*G_P)[j+1][i] != ( (*G_P)[j+1][0])*crc_polynomial_pattern[i]) //xor
+                        (*G_P)[j][i-1]=1;
+                }
+
+                if(0 != ( (*G_P)[j+1][0])*crc_polynomial_pattern[P]) //xor
+                        (*G_P)[j][P-1]=1;
+            }
+        }
+printf("G_P=\n");
+        for(i=0; i<A; i++)
+        {
+            for(j=0; j<P; j++)
+            {
+                printf("%i ", (int)(*G_P)[i][j]);
+            }
+            printf("\n");
+        }
+
+}

openair1/PHY/CODING/nrPolar_tools/main_pucch.c

+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+
+#include "nr_polar_defs.h"
+#include "nr_polar_pucch_defs.h"
+
+void PUCCH_encoder(uint8_t a[], uint8_t A, uint8_t G, uint16_t* E_r, uint8_t** f);
+
+int main()
+{
+    uint16_t E_r;
+    uint8_t* f;
+    uint8_t A=32; //16, 32, 64, 128, 256, 512, 1024 Payload length
+    uint8_t G = 54; //, 108, 216, 432, 864, 1728, 3456, 6912, 13824}; encoded block length
+
+    uint8_t j;
+
+    uint8_t* a = (uint8_t *)malloc(sizeof(uint8_t)*A);
+    if (a == NULL)
+    {
+        fprintf(stderr, "malloc failed\n");
+        exit(-1);
+    }
+
+    printf("DEBUG: Send ");
+    for (j=0; j<A; j++) //create the message to encode
+    {
+        //a[j]=rand()%2;
+        a[j]=1; // ONLY ONES FOR TEST, otherwise random
+        printf("%i", a[j]);
+    }
+    printf("\n");
+
+    PUCCH_encoder(a, A, G, &E_r, &f);
+
+
+    return 0;
+}

openair1/PHY/CODING/nrPolar_tools/nr_bitwise_operations.c

+#include "PHY/CODING/nrPolar_tools/nr_polar_defs.h"
+
+void nr_byte2bit(uint8_t *array, uint8_t arraySize, uint8_t *bitArray){//First 2 parameters are in bytes.
+
+	for (int i=0; i<arraySize; i++){
+		bitArray[(7+(i*8))] = ( array[i]>>0 & 0x01);
+		bitArray[(6+(i*8))] = ( array[i]>>1 & 0x01);
+		bitArray[(5+(i*8))] = ( array[i]>>2 & 0x01);
+		bitArray[(4+(i*8))] = ( array[i]>>3 & 0x01);
+		bitArray[(3+(i*8))] = ( array[i]>>4 & 0x01);
+		bitArray[(2+(i*8))] = ( array[i]>>5 & 0x01);
+		bitArray[(1+(i*8))] = ( array[i]>>6 & 0x01);
+		bitArray[  (i*8)  ] = ( array[i]>>7 & 0x01);
+	}
+
+}

openair1/PHY/CODING/nrPolar_tools/nr_polar_bit_insertion.c

+#include "PHY/CODING/nrPolar_tools/nr_polar_defs.h"
+
+void nr_polar_bit_insertion(uint8_t *input, uint8_t *output, uint16_t N, uint16_t K,
+		uint16_t *Q_I_N, uint16_t *Q_PC_N, uint8_t n_PC){
+
+	uint16_t k=0;
+	uint8_t flag;
+
+	if (n_PC>0) {
+		/*
+		 *
+		 */
+	} else {
+		for (int n=0; n<=N-1; n++) {
+			flag=0;
+			for (int m=0; m<=(K+n_PC)-1; m++) {
+				if ( n == Q_I_N[m]) {
+					flag=1;
+					break;
+				}
+			}
+			if (flag) { // n ϵ Q_I_N
+				output[n]=input[k];
+				k++;
+			} else {
+				output[n] = 0;
+			}
+		}
+	}
+
+}

openair1/PHY/CODING/nrPolar_tools/nr_polar_bit_insertion_2.c

+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+#include <stdint.h>
+
+void nr_polar_bit_insertion_2(uint8_t* u, uint8_t* b, uint8_t* info_bit_pattern, uint8_t* PC_bit_pattern, uint16_t N)
+{
+        int PC_circular_buffer_length=5;
+
+        int i, j;
+        int k=0;
+
+        int* y = (int*) malloc(sizeof(int)*PC_circular_buffer_length);
+        if (y == NULL)
+        {
+            fprintf(stderr, "malloc failed\n");
+            exit(-1);
+        }
+        for(i=0; i<PC_circular_buffer_length; i++)
+        {
+            y[i]=0;
+        }
+
+        int tempToShift;
+        //for n=0:N-1
+        printf("u = ");
+        for(i=0; i<N; i++)
+        {
+            //y = [y(2:end),y(1)];
+            tempToShift=y[0];
+            for (j=0; j<PC_circular_buffer_length-1; j++)
+            {
+                y[j]=y[j+1];
+            }
+            y[PC_circular_buffer_length-1]=tempToShift;
+
+            //if info_bit_pattern(n+1)
+            //    if PC_bit_pattern(n+1)
+            //        u(n+1) = y(1);
+            //    else
+            //        u(n+1) = b(k+1);
+            //        k=k+1;
+            //        y(1) = xor(y(1),u(n+1));
+            if (info_bit_pattern[i])
+            {
+                if (PC_bit_pattern[i])
+                {
+                    u[i] = y[1];
+                } else
+                {
+                    u[i] = b[k];
+                    k++;
+                    y[1] = ( y[1]!=u[i]);
+                }
+            } else
+            {
+                u[i]=0;
+            }
+            printf("%i ", u[i]);
+        }
+
+        free(y);
+}

openair1/PHY/CODING/nrPolar_tools/nr_polar_channel_interleaver_pattern.c

+#include "PHY/CODING/nrPolar_tools/nr_polar_defs.h"
+
+void nr_polar_channel_interleaver_pattern(uint16_t *cip, uint8_t I_BIL, uint16_t E){
+	
+	if (I_BIL == 1) {
+		uint16_t T=0, k;
+		while( ((T/2)*(T+1)) < E ) T++;
+		
+		
+		int16_t **v = malloc(T * sizeof(*v));
+		for (int i = 0; i <= T-1; i++) v[i] = malloc((T-i) * sizeof(*(v[i])));
+		
+		k=0;
+		for (int i = 0; i <= T-1; i++) {
+			for (int j = 0; j <= (T-1)-i; j++) {
+				if (k<E) {
+					v[i][j] = k;
+				} else {
+					v[i][j] = (-1);
+				}
+				k++;					
+			}
+		}
+		
+		k=0;
+		for (int j = 0; j <= T-1; j++) {
+					for (int i = 0; i <= (T-1)-j; i++) {
+						if ( v[i][j] != (-1) ) {
+							cip[k]=v[i][j];
+							k++;
+						}
+					}
+				}
+		
+		for (int i = 0; i <= T-1; i++) free(v[i]);
+		free(v);
+		
+	} else {
+		for (int i=0; i<=E-1; i++) cip[i]=i;
+	}
+	
+}

openair1/PHY/CODING/nrPolar_tools/nr_polar_crc.c

+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+#include <stdint.h>
+
+void nr_polar_crc(uint8_t* a, uint8_t A, uint8_t P, uint8_t** G_P, uint8_t** b)
+{
+    int i, j;
+    int* temp_b = (int*) malloc(sizeof(int)*P);
+    if (temp_b == NULL)
+    {
+        fprintf(stderr, "malloc failed\n");
+        exit(-1);
+    }
+    printf("temp = ");
+    for(i=0; i<P; i++)
+    {
+        temp_b[i]=0;
+        for(j=0; j<A; j++)
+        {
+            temp_b[i]=temp_b[i] + a[j]*G_P[j][i];
+        }
+        temp_b[i]=temp_b[i]%2;
+        printf("%i ", temp_b[i]);
+    }
+
+    *b = (uint8_t*) malloc(sizeof(uint8_t)*(A+P));
+    if (*b == NULL)
+    {
+        fprintf(stderr, "malloc failed\n");
+        exit(-1);
+    }
+    printf("\nb = ");
+    for(i=0; i<A; i++)
+    {
+        (*b)[i]=a[i];
+        printf("%i", (*b)[i]);
+    }
+    for(i=A; i<A+P; i++)
+    {
+        (*b)[i]=temp_b[i-A];
+        printf("%i", (*b)[i]);
+    }
+
+    free(temp_b);
+}

openair1/PHY/CODING/nrPolar_tools/nr_polar_decoder.c

+#include "PHY/CODING/nrPolar_tools/nr_polar_defs.h"
+#include "PHY/CODING/nrPolar_tools/nr_polar_pbch_defs.h"
+
+/*
+ * Return values:
+ *  0 --> Success
+ * -1 --> All list entries have failed the CRC checks
+ */
+
+int8_t polar_decoder(double *input, uint8_t *output, t_nrPolar_params *polarParams, uint8_t listSize,
+		double *aPrioriPayload, uint8_t pathMetricAppr){
+
+	uint8_t ***bit = nr_alloc_uint8_t_3D_array(polarParams->N, (polarParams->n+1), 2*listSize);
+	uint8_t **bitUpdated = nr_alloc_uint8_t_2D_array(polarParams->N, (polarParams->n+1)); //0=False, 1=True
+	uint8_t **llrUpdated = nr_alloc_uint8_t_2D_array(polarParams->N, (polarParams->n+1)); //0=False, 1=True
+	double ***llr = nr_alloc_double_3D_array(polarParams->N, (polarParams->n+1), 2*listSize);
+	uint8_t **crcChecksum = nr_alloc_uint8_t_2D_array(polarParams->crcParityBits, 2*listSize);
+	double *pathMetric = malloc(sizeof(double)*(2*listSize));
+	uint8_t *crcState = malloc(sizeof(uint8_t)*(2*listSize)); //0=False, 1=True
+
+	for (int i=0; i<(2*listSize); i++) {
+		pathMetric[i] = 0;
+		crcState[i]=1;
+	}
+	for (int i=0; i<polarParams->N; i++) {
+		llrUpdated[i][polarParams->n]=1;
+		bitUpdated[i][0]=((polarParams->information_bit_pattern[i]+1) % 2);
+	}
+
+	uint8_t **crc_generator_matrix=crc24c_generator_matrix(polarParams->payloadBits); //G_P
+
+	uint8_t **extended_crc_generator_matrix = malloc(polarParams->K * sizeof(uint8_t *)); //G_P3
+	uint8_t **tempECGM = malloc(polarParams->K * sizeof(uint8_t *)); //G_P2
+	for (int i = 0; i < polarParams->K; i++){
+		extended_crc_generator_matrix[i] = malloc(polarParams->crcParityBits * sizeof(uint8_t));
+		tempECGM[i] = malloc(polarParams->crcParityBits * sizeof(uint8_t));
+	}
+
+	for (int i=0; i<polarParams->payloadBits; i++) {
+		for (int j=0; j<polarParams->crcParityBits; j++) {
+			tempECGM[i][j]=crc_generator_matrix[i][j];
+		}
+	}
+	for (int i=polarParams->payloadBits; i<polarParams->K; i++) {
+			for (int j=0; j<polarParams->crcParityBits; j++) {
+				if( (i-polarParams->payloadBits) == j ){
+					tempECGM[i][j]=1;
+				} else {
+					tempECGM[i][j]=0;
+				}
+			}
+	}
+
+	for (int i=0; i<polarParams->K; i++) {
+		for (int j=0; j<polarParams->crcParityBits; j++) {
+			extended_crc_generator_matrix[i][j]=tempECGM[polarParams->interleaving_pattern[i]][j];
+		}
+	}
+
+	//The index of the last 1-valued bit that appears in each column.
+	uint16_t last1ind[polarParams->crcParityBits];
+	for (int j=0; j<polarParams->crcParityBits; j++) {
+			for (int i=0; i<polarParams->K; i++) {
+				if (extended_crc_generator_matrix[i][j]==1) last1ind[j]=i;
+			}
+	}
+
+	double *d_tilde = malloc(sizeof(double) * polarParams->N);
+	nr_polar_rate_matching(input, d_tilde, polarParams->rate_matching_pattern, polarParams->K, polarParams->N, polarParams->encoderLength);
+	for (int j = 0; j < polarParams->N; j++) llr[j][polarParams->n][0]=d_tilde[j];
+
+
+	/*
+	 * SCL polar decoder.
+	 */
+
+	uint32_t nonFrozenBit=0;
+	uint8_t currentListSize=1;
+	uint8_t decoderIterationCheck=0;
+	int16_t checkCrcBits=-1;
+	uint8_t listIndex[2*listSize], copyIndex;
+
+	for (uint16_t currentBit=0; currentBit<polarParams->N; currentBit++){
+		updateLLR(llr, llrUpdated, bit, bitUpdated, currentListSize, currentBit, 0, polarParams->N, (polarParams->n+1), pathMetricAppr);
+		if (polarParams->information_bit_pattern[currentBit]==0) { //Frozen bit.
+			updatePathMetric(pathMetric, llr, currentListSize, 0, currentBit, pathMetricAppr); //approximation=0 --> 11b, approximation=1 --> 12
+		} else { //Information or CRC bit.
+			if ( (polarParams->interleaving_pattern[nonFrozenBit] <= polarParams->payloadBits) && (aPrioriPayload[polarParams->interleaving_pattern[nonFrozenBit]] == 0) ) {
+				//Information bit with known value of "0".
+				updatePathMetric(pathMetric, llr, currentListSize, 0, currentBit, pathMetricAppr);
+				bitUpdated[currentBit][0]=1; //0=False, 1=True
+			} else if ( (polarParams->interleaving_pattern[nonFrozenBit] <= polarParams->payloadBits) && (aPrioriPayload[polarParams->interleaving_pattern[nonFrozenBit]] == 1) ) {
+				//Information bit with known value of "1".
+				updatePathMetric(pathMetric, llr, currentListSize, 1, currentBit, pathMetricAppr);
+				for (uint8_t i=0; i<currentListSize; i++) bit[currentBit][0][i]=1;
+				bitUpdated[currentBit][0]=1;
+				updateCrcChecksum(crcChecksum, extended_crc_generator_matrix, currentListSize, nonFrozenBit, polarParams->crcParityBits);
+			} else {
+				updatePathMetric2(pathMetric, llr, currentListSize, currentBit, pathMetricAppr);
+
+				for (int i = 0; i < currentListSize; i++) {
+					for (int j = 0; j < polarParams->N; j++) {
+						for (int k = 0; k < (polarParams->n+1); k++) {
+							bit[j][k][i+currentListSize]=bit[j][k][i];
+							llr[j][k][i+currentListSize]=llr[j][k][i];}}}
+				for (int i = 0; i < currentListSize; i++) {
+					bit[currentBit][0][i]=0;
+					crcState[i+currentListSize]=crcState[i];
+				}
+				for (int i = currentListSize; i < 2*currentListSize; i++) bit[currentBit][0][i]=1;
+				bitUpdated[currentBit][0]=1;
+				updateCrcChecksum2(crcChecksum, extended_crc_generator_matrix, currentListSize, nonFrozenBit, polarParams->crcParityBits);
+				currentListSize*=2;
+
+				//Keep only the best "listSize" number of entries.
+				if (currentListSize > listSize) {
+					for (uint8_t i = 0; i < 2*listSize; i++) listIndex[i]=i;
+					nr_sort_asc_double_1D_array_ind(pathMetric, listIndex, currentListSize);
+
+					//sort listIndex[listSize, ..., 2*listSize-1] in descending order.
+					uint8_t swaps, tempInd;
+					for (uint8_t i = 0; i < listSize; i++) {
+						swaps = 0;
+						for (uint8_t j = listSize; j < (2*listSize - i) - 1; j++) {
+							if (listIndex[j+1] > listIndex[j]) {
+								tempInd = listIndex[j];
+								listIndex[j] = listIndex[j + 1];
+								listIndex[j + 1] = tempInd;
+								swaps++;
+							}
+						}
+						if (swaps == 0)
+							break;
+					}
+
+					//First, backup the best "listSize" number of entries.
+					for (int k=(listSize-1); k>0; k--) {
+						for (int i=0; i<polarParams->N; i++) {
+							for (int j=0; j<(polarParams->n+1); j++) {
+								bit[i][j][listIndex[(2*listSize-1)-k]]=bit[i][j][listIndex[k]];
+								llr[i][j][listIndex[(2*listSize-1)-k]]=llr[i][j][listIndex[k]];
+							}
+						}
+					}
+					for (int k=(listSize-1); k>0; k--) {
+						for (int i = 0; i < polarParams->crcParityBits; i++) {
+							crcChecksum[i][listIndex[(2*listSize-1)-k]] = crcChecksum[i][listIndex[k]];
+						}
+					}
+					for (int k=(listSize-1); k>0; k--) crcState[listIndex[(2*listSize-1)-k]]=crcState[listIndex[k]];
+
+					//Copy the best "listSize" number of entries to the first indices.
+					for (int k = 0; k < listSize; k++) {
+						if (k > listIndex[k]) {
+							copyIndex = listIndex[(2*listSize-1)-k];
+						} else { //Use the backup.
+							copyIndex = listIndex[k];
+						}
+						for (int i = 0; i < polarParams->N; i++) {
+							for (int j = 0; j < (polarParams->n + 1); j++) {
+								bit[i][j][k] = bit[i][j][copyIndex];
+								llr[i][j][k] = llr[i][j][copyIndex];
+							}
+						}
+					}
+					for (int k = 0; k < listSize; k++) {
+						if (k > listIndex[k]) {
+							copyIndex = listIndex[(2*listSize-1)-k];
+						} else { //Use the backup.
+							copyIndex = listIndex[k];
+						}
+						for (int i = 0; i < polarParams->crcParityBits; i++) {
+							crcChecksum[i][k]=crcChecksum[i][copyIndex];
+						}
+					}
+					for (int k = 0; k < listSize; k++) {
+						if (k > listIndex[k]) {
+							copyIndex = listIndex[(2*listSize-1)-k];
+						} else { //Use the backup.
+							copyIndex = listIndex[k];
+						}
+						crcState[k]=crcState[copyIndex];
+					}
+					currentListSize = listSize;
+				}
+			}
+
+			for (int i=0; i<polarParams->crcParityBits; i++) {
+				if (last1ind[i]==nonFrozenBit) {
+					checkCrcBits=i;
+					break;
+				}
+			}
+
+			if ( checkCrcBits > (-1) ) {
+				for (uint8_t i = 0; i < currentListSize; i++) {
+					if (crcChecksum[checkCrcBits][i]==1) {
+						crcState[i]=0; //0=False, 1=True
+					}
+				}
+			}
+
+			for (uint8_t i = 0; i < currentListSize; i++) decoderIterationCheck+=crcState[i];
+			if (decoderIterationCheck==0) {
+				//perror("[SCL polar decoder] All list entries have failed the CRC checks.");
+				free(crc_generator_matrix);
+				free(d_tilde);
+				free(pathMetric);
+				nr_free_uint8_t_3D_array(bit, polarParams->N, (polarParams->n+1));
+				nr_free_double_3D_array(llr, polarParams->N, (polarParams->n+1));
+				nr_free_uint8_t_2D_array(crcChecksum, polarParams->crcParityBits);
+				return(-1);
+			}
+
+			nonFrozenBit++;
+			decoderIterationCheck=0;
+			checkCrcBits=-1;
+		}
+	}
+
+	for (uint8_t i = 0; i < 2*listSize; i++) listIndex[i]=i;
+	nr_sort_asc_double_1D_array_ind(pathMetric, listIndex, currentListSize);
+
+	uint8_t *nr_polar_uHat = malloc(sizeof(uint8_t) * polarParams->N);
+	uint8_t *nr_polar_cHat = malloc(sizeof(uint8_t) * polarParams->K);
+	uint8_t *nr_polar_bHat = malloc(sizeof(uint8_t) * polarParams->K);
+	for (uint8_t i = 0; i < fmin(listSize, (pow(2,polarParams->crcCorrectionBits)) ); i++) {
+		if ( crcState[listIndex[i]] == 1 ) {
+			for (int j = 0; j < polarParams->N; j++) nr_polar_uHat[j]=bit[j][0][listIndex[i]];
+
+			//Extract the information bits (û to ĉ)
+			nr_polar_info_bit_extraction(nr_polar_uHat, nr_polar_cHat, polarParams->information_bit_pattern, polarParams->N);
+
+			//Deinterleaving (ĉ to b)
+			nr_polar_deinterleaver(nr_polar_cHat, nr_polar_bHat, polarParams->interleaving_pattern, polarParams->K);
+
+			//Remove the CRC (â)
+			for (int j = 0; j < polarParams->payloadBits; j++) output[j]=nr_polar_bHat[j];
+
+			break;
+		}
+	}
+
+	free(crc_generator_matrix);
+	free(d_tilde);
+	free(pathMetric);
+	free(nr_polar_uHat);
+	free(nr_polar_cHat);
+	free(nr_polar_bHat);
+	nr_free_uint8_t_3D_array(bit, polarParams->N, (polarParams->n+1));
+	nr_free_double_3D_array(llr, polarParams->N, (polarParams->n+1));
+	nr_free_uint8_t_2D_array(crcChecksum, polarParams->crcParityBits);
+	return(0);
+}

openair1/PHY/CODING/nrPolar_tools/nr_polar_decoding_tools.c

+#include "PHY/CODING/nrPolar_tools/nr_polar_defs.h"
+
+void updateLLR(double ***llr, uint8_t **llrU, uint8_t ***bit, uint8_t **bitU,
+		uint8_t listSize, uint16_t row, uint16_t col, uint16_t xlen, uint8_t ylen, uint8_t approximation) {
+	uint16_t offset = (xlen/(pow(2,(ylen-col-1))));
+	for (uint8_t i=0; i<listSize; i++) {
+		if (( (row) % (2*offset) ) >= offset ) {
+			if(bitU[row-offset][col]==0) updateBit(bit, bitU, listSize, (row-offset), col, xlen, ylen);
+			if(llrU[row-offset][col+1]==0) updateLLR(llr, llrU, bit, bitU, listSize, (row-offset), (col+1), xlen, ylen, approximation);
+			if(llrU[row][col+1]==0) updateLLR(llr, llrU, bit, bitU, listSize, row, (col+1), xlen, ylen, approximation);
+			llr[row][col][i] = (pow((-1),bit[row-offset][col][i])*llr[row-offset][col+1][i]) + llr[row][col+1][i];
+		} else {
+			if(llrU[row][col+1]==0) updateLLR(llr, llrU, bit, bitU, listSize, row, (col+1), xlen, ylen, approximation);
+			if(llrU[row+offset][col+1]==0) updateLLR(llr, llrU, bit, bitU, listSize, (row+offset), (col+1), xlen, ylen, approximation);
+			computeLLR(llr, row, col, i, offset, approximation);
+		}
+	}
+
+	llrU[row][col]=1;
+}
+
+void updateBit(uint8_t ***bit, uint8_t **bitU, uint8_t listSize, uint16_t row,
+		uint16_t col, uint16_t xlen, uint8_t ylen) {
+	uint16_t offset = ( xlen/(pow(2,(ylen-col))) );
+
+	for (uint8_t i=0; i<listSize; i++) {
+		if (( (row) % (2*offset) ) >= offset ) {
+			if (bitU[row][col-1]==0) updateBit(bit, bitU, listSize, row, (col-1), xlen, ylen);
+			bit[row][col][i] = bit[row][col-1][i];
+		} else {
+			if (bitU[row][col-1]==0) updateBit(bit, bitU, listSize, row, (col-1), xlen, ylen);
+			if (bitU[row+offset][col-1]==0) updateBit(bit, bitU, listSize, (row+offset), (col-1), xlen, ylen);
+			bit[row][col][i] = ( (bit[row][col-1][i]+bit[row+offset][col-1][i]) % 2);
+		}
+	}
+
+	bitU[row][col]=1;
+}
+
+void updatePathMetric(double *pathMetric, double ***llr, uint8_t listSize, uint8_t bitValue,
+		uint16_t row, uint8_t approximation) {
+
+	if (approximation) { //eq. (12)
+		for (uint8_t i=0; i<listSize; i++) {
+			if ((2*bitValue) != ( 1 - copysign(1.0,llr[row][0][i]) )) pathMetric[i] += fabs(llr[row][0][i]);
+		}
+	} else { //eq. (11b)
+		int8_t multiplier = (2*bitValue) - 1;
+		for (uint8_t i=0; i<listSize; i++) pathMetric[i] += log ( 1 + exp(multiplier*llr[row][0][i]) ) ;
+	}
+
+}
+
+void updatePathMetric2(double *pathMetric, double ***llr, uint8_t listSize, uint16_t row, uint8_t appr) {
+
+	double *tempPM = malloc(sizeof(double) * listSize);
+	for (int i=0; i < listSize; i++) tempPM[i]=pathMetric[i];
+
+	uint8_t bitValue = 0;
+	if (appr) { //eq. (12)
+		for (uint8_t i = 0; i < listSize; i++) {
+			if ((2 * bitValue) != (1 - copysign(1.0, llr[row][0][i]))) pathMetric[i] += fabs(llr[row][0][i]);
+		}
+	} else { //eq. (11b)
+		int8_t multiplier = (2 * bitValue) - 1;
+		for (uint8_t i = 0; i < listSize; i++) pathMetric[i] += log(1 + exp(multiplier * llr[row][0][i]));
+	}
+
+	bitValue = 1;
+	if (appr) { //eq. (12)
+		for (uint8_t i = listSize; i < 2*listSize; i++) {
+			if ((2 * bitValue) != (1 - copysign(1.0, llr[row][0][(i-listSize)]))) pathMetric[i] = tempPM[(i-listSize)] + fabs(llr[row][0][(i-listSize)]);
+		}
+	} else { //eq. (11b)
+		int8_t multiplier = (2 * bitValue) - 1;
+		for (uint8_t i = listSize; i < 2*listSize; i++) pathMetric[i] = tempPM[(i-listSize)] + log(1 + exp(multiplier * llr[row][0][(i-listSize)]));
+	}
+
+	free(tempPM);
+
+}
+
+void computeLLR(double ***llr, uint16_t row, uint16_t col, uint8_t i,
+		uint16_t offset, uint8_t approximation) {
+
+	double a = llr[row][col + 1][i];
+	double absA = fabs(a);
+	double b = llr[row + offset][col + 1][i];
+	double absB = fabs(b);
+
+	if (approximation || isinf(absA) || isinf(absB)) { //eq. (9)
+		llr[row][col][i] = copysign(1.0, a) * copysign(1.0, b) * fmin(absA, absB);
+	} else { //eq. (8a)
+		llr[row][col][i] = log((exp(a + b) + 1) / (exp(a) + exp(b)));
+	}
+
+}
+
+void updateCrcChecksum(uint8_t **crcChecksum, uint8_t **crcGen,
+		uint8_t listSize, uint32_t i2, uint8_t len) {
+	for (uint8_t i = 0; i < listSize; i++) {
+		for (uint8_t j = 0; j < len; j++) {
+			crcChecksum[j][i] = ( (crcChecksum[j][i] + crcGen[i2][j]) % 2 );
+		}
+	}
+}
+
+void updateCrcChecksum2(uint8_t **crcChecksum, uint8_t **crcGen,
+		uint8_t listSize, uint32_t i2, uint8_t len) {
+	for (uint8_t i = 0; i < listSize; i++) {
+		for (uint8_t j = 0; j < len; j++) {
+			crcChecksum[j][i+listSize] = ( (crcChecksum[j][i] + crcGen[i2][j]) % 2 );
+		}
+	}
+}

openair1/PHY/CODING/nrPolar_tools/nr_polar_defs.h

+#ifndef __NR_POLAR_DEFS__H__
+#define __NR_POLAR_DEFS__H__
+
+#include <math.h>
+#include <stdio.h>
+#include <stdint.h>
+#include <stdlib.h>
+#include <string.h>
+
+static const uint8_t nr_polar_subblock_interleaver_pattern[32] = { 0, 1, 2, 4, 3, 5, 6, 7, 8, 16, 9, 17, 10, 18, 11, 19, 12, 20, 13, 21, 14, 22, 15, 23, 24, 25, 26, 28, 27, 29, 30, 31 };
+
+typedef struct nrPolar_params {
+	uint8_t n_max;
+	uint8_t i_il;
+	uint8_t n_pc;
+	uint8_t n_pc_wm;
+	uint8_t i_bil;
+	uint16_t payloadBits;
+	uint16_t encoderLength;
+	uint8_t crcParityBits;
+	uint8_t crcCorrectionBits;
+	uint16_t K;
+	uint16_t N;
+	uint8_t n;
+
+	uint16_t *interleaving_pattern;
+	uint16_t *rate_matching_pattern;
+	uint16_t *Q_0_Nminus1;
+	int16_t *Q_I_N;
+	int16_t *Q_F_N;
+	int16_t *Q_PC_N;
+	uint8_t *information_bit_pattern;
+	uint16_t *channel_interleaver_pattern;
+
+	uint8_t **crc_generator_matrix; //G_P
+	uint8_t **G_N;
+} t_nrPolar_params;
+
+void polar_encoder(uint8_t *input, uint8_t *channel_input, t_nrPolar_params* polarParams);
+
+int8_t polar_decoder(double *input, uint8_t *output, t_nrPolar_params *polarParams,
+		uint8_t listSize, double *aPrioriPayload, uint8_t pathMetricAppr);
+
+void nr_polar_init(t_nrPolar_params* polarParams, int messageType);
+
+uint8_t** nr_polar_kronecker_power_matrices(uint8_t n);
+
+uint16_t* nr_polar_sequence_pattern(uint8_t n);
+
+uint32_t nr_polar_output_length(uint16_t K, uint16_t E, uint8_t n_max);
+
+void nr_polar_channel_interleaver_pattern(uint16_t *cip, uint8_t I_BIL,
+		uint16_t E);
+
+void nr_polar_rate_matching_pattern(uint16_t *rmp, uint16_t *J, uint8_t *P_i_,
+		uint16_t K, uint16_t N, uint16_t E);
+
+void nr_polar_rate_matching(double *input, double *output, uint16_t *rmp,
+		uint16_t K, uint16_t N, uint16_t E);
+
+void nr_polar_rate_matcher(uint8_t *input, unsigned char *output, uint16_t *pattern, uint16_t size);
+
+void nr_polar_interleaving_pattern(uint16_t K, uint8_t I_IL, uint16_t *PI_k_);
+
+void nr_polar_interleaver(uint8_t *input, uint8_t *output, uint16_t *pattern,
+		uint16_t size);
+
+void nr_polar_deinterleaver(uint8_t *input, uint8_t *output, uint16_t *pattern,
+		uint16_t size);
+
+void nr_polar_info_bit_pattern(uint8_t *ibp, uint16_t *Q_I_N, int16_t *Q_F_N,
+		uint16_t *J, uint16_t *Q_0_Nminus1, uint16_t K, uint16_t N, uint16_t E,
+		uint8_t n_PC);
+
+void nr_polar_info_bit_extraction(uint8_t *input, uint8_t *output,
+		uint8_t *pattern, uint16_t size);
+
+void nr_byte2bit(uint8_t *array, uint8_t arraySize, uint8_t *bitArray);
+
+void nr_polar_bit_insertion(uint8_t *input, uint8_t *output, uint16_t N,
+		uint16_t K, uint16_t *Q_I_N, uint16_t *Q_PC_N, uint8_t n_PC);
+
+void nr_matrix_multiplication_uint8_t_1D_uint8_t_2D(uint8_t *matrix1, uint8_t **matrix2,
+		uint8_t *output, uint16_t row, uint16_t col);
+
+uint8_t ***nr_alloc_uint8_t_3D_array(uint16_t xlen, uint16_t ylen,
+		uint16_t zlen);
+uint8_t **nr_alloc_uint8_t_2D_array(uint16_t xlen, uint16_t ylen);
+double ***nr_alloc_double_3D_array(uint16_t xlen, uint16_t ylen, uint16_t zlen);
+
+void nr_free_uint8_t_3D_array(uint8_t ***input, uint16_t xlen, uint16_t ylen);
+void nr_free_uint8_t_2D_array(uint8_t **input, uint16_t xlen);
+void nr_free_double_3D_array(double ***input, uint16_t xlen, uint16_t ylen);
+
+void updateLLR(double ***llr, uint8_t **llrU, uint8_t ***bit, uint8_t **bitU,
+		uint8_t listSize, uint16_t row, uint16_t col, uint16_t xlen,
+		uint8_t ylen, uint8_t approximation);
+void updateBit(uint8_t ***bit, uint8_t **bitU, uint8_t listSize, uint16_t row,
+		uint16_t col, uint16_t xlen, uint8_t ylen);
+void updatePathMetric(double *pathMetric, double ***llr, uint8_t listSize,
+		uint8_t bitValue, uint16_t row, uint8_t approximation);
+void updatePathMetric2(double *pathMetric, double ***llr, uint8_t listSize,
+		uint16_t row, uint8_t approximation);
+void computeLLR(double ***llr, uint16_t row, uint16_t col, uint8_t i,
+		uint16_t offset, uint8_t approximation);
+void updateCrcChecksum(uint8_t **crcChecksum, uint8_t **crcGen,
+		uint8_t listSize, uint32_t i2, uint8_t len);
+void updateCrcChecksum2(uint8_t **crcChecksum, uint8_t **crcGen,
+		uint8_t listSize, uint32_t i2, uint8_t len);
+void nr_sort_asc_double_1D_array_ind(double *matrix, uint8_t *ind, uint8_t len);
+
+#endif

openair1/PHY/CODING/nrPolar_tools/nr_polar_encoder.c

+#include "PHY/CODING/nrPolar_tools/nr_polar_defs.h"
+#include "PHY/CODING/nrPolar_tools/nr_polar_pbch_defs.h"
+
+void polar_encoder(uint8_t *input, uint8_t *channel_input, t_nrPolar_params *polarParams){
+	/*//Create the Transport Block.
+	unsigned int payload=0xb3f02c82;
+	uint8_t pbchTransportBlockSize = ( polarParams->K / (8*sizeof(uint8_t)) );
+	uint8_t *pbchTransportBlock = malloc(pbchTransportBlockSize);
+	memcpy(pbchTransportBlock,&payload,sizeof(payload));
+
+	//Attach CRC to the Transport Block. (a to b)
+	uint32_t crc = crc24c(&payload, NR_POLAR_PBCH_PAYLOAD_BITS)>>8;
+	pbchTransportBlock[NR_POLAR_PBCH_PAYLOAD_BITS>>3] = ((uint8_t*)&crc)[2];
+	pbchTransportBlock[1+(NR_POLAR_PBCH_PAYLOAD_BITS>>3)] = ((uint8_t*)&crc)[1];
+	pbchTransportBlock[2+(NR_POLAR_PBCH_PAYLOAD_BITS>>3)] = ((uint8_t*)&crc)[0];*/
+
+	/*
+	 * Bytewise operations
+	 */
+
+	//Calculate CRC.
+	uint8_t *nr_polar_crc = malloc(sizeof(uint8_t) * polarParams->crcParityBits);
+	nr_matrix_multiplication_uint8_t_1D_uint8_t_2D(input, polarParams->crc_generator_matrix,
+			nr_polar_crc, polarParams->payloadBits, polarParams->crcParityBits);
+	for (uint8_t i = 0; i < polarParams->crcParityBits; i++) nr_polar_crc[i] = (nr_polar_crc[i] % 2);
+
+	//Attach CRC to the Transport Block. (a to b)
+	uint8_t *nr_polar_b = malloc(sizeof(uint8_t) * polarParams->K);
+	for (uint16_t i = 0; i < polarParams->payloadBits; i++) nr_polar_b[i] = input[i];
+	for (uint16_t i = polarParams->payloadBits; i < polarParams->K; i++) nr_polar_b[i]= nr_polar_crc[i-(polarParams->payloadBits)];
+
+	//Interleaving (c to c')
+	uint8_t *nr_polar_cPrime = malloc(sizeof(uint8_t) * polarParams->K);
+	nr_polar_interleaver(nr_polar_b, nr_polar_cPrime, polarParams->interleaving_pattern, polarParams->K);
+
+	//Bit insertion (c' to u)
+	uint8_t *nr_polar_u = malloc(sizeof(uint8_t) * polarParams->N);
+	nr_polar_bit_insertion(nr_polar_cPrime, nr_polar_u, polarParams->N, polarParams->K,
+			polarParams->Q_I_N, polarParams->Q_PC_N, polarParams->n_pc);
+
+	//Encoding (u to d)
+	uint8_t *pbch_polar_encoder_output = malloc(sizeof(uint8_t) * polarParams->N);
+	nr_matrix_multiplication_uint8_t_1D_uint8_t_2D(nr_polar_u, polarParams->G_N, pbch_polar_encoder_output, polarParams->N, polarParams->N);
+	for (uint16_t i = 0; i < polarParams->N; i++) pbch_polar_encoder_output[i] = (pbch_polar_encoder_output[i] % 2);
+
+	//Rate matching
+	//Sub-block interleaving (d to y) and Bit selection (y to e)
+	nr_polar_rate_matcher(pbch_polar_encoder_output, channel_input, polarParams->rate_matching_pattern, polarParams->encoderLength);
+
+	//free(pbchTransportBlock);
+	free(nr_polar_crc);
+	free(nr_polar_b);
+	free(nr_polar_cPrime);
+	free(nr_polar_u);
+	free(pbch_polar_encoder_output);
+}

openair1/PHY/CODING/nrPolar_tools/nr_polar_info_bit_pattern.c

+#include "PHY/CODING/nrPolar_tools/nr_polar_defs.h"
+
+void nr_polar_info_bit_pattern(uint8_t *ibp, uint16_t *Q_I_N, int16_t *Q_F_N,
+		uint16_t *J, uint16_t *Q_0_Nminus1, uint16_t K, uint16_t N, uint16_t E,
+		uint8_t n_PC) {
+
+	int16_t *Q_Ftmp_N = malloc(sizeof(int16_t) * (N + 1)); // Last element shows the final
+	int16_t *Q_Itmp_N = malloc(sizeof(int16_t) * (N + 1)); // array index assigned a value.
+
+	for (int i = 0; i <= N; i++) {
+		Q_Ftmp_N[i] = -1; // Empty array.
+		Q_Itmp_N[i] = -1;
+	}
+
+	uint8_t flag;
+	uint16_t limit, ind;
+
+	if (E < N) {
+		if ((K / (double) E) <= (7.0 / 16)) { //puncturing
+			for (int n = 0; n <= N - E - 1; n++) {
+				ind = Q_Ftmp_N[N] + 1;
+				Q_Ftmp_N[ind] = J[n];
+				Q_Ftmp_N[N] = Q_Ftmp_N[N] + 1;
+			}
+
+			if ((E / (double) N) >= (3.0 / 4)) {
+				limit = ceil((double) (3 * N - 2 * E) / 4);
+				for (int n = 0; n <= limit - 1; n++) {
+					ind = Q_Ftmp_N[N] + 1;
+					Q_Ftmp_N[ind] = n;
+					Q_Ftmp_N[N] = Q_Ftmp_N[N] + 1;
+				}
+			} else {
+				limit = ceil((double) (9 * N - 4 * E) / 16);
+				for (int n = 0; n <= limit - 1; n++) {
+					ind = Q_Ftmp_N[N] + 1;
+					Q_Ftmp_N[ind] = n;
+					Q_Ftmp_N[N] = Q_Ftmp_N[N] + 1;
+				}
+			}
+		} else { //shortening
+			for (int n = E; n <= N - 1; n++) {
+				ind = Q_Ftmp_N[N] + 1;
+				Q_Ftmp_N[ind] = J[n];
+				Q_Ftmp_N[N] = Q_Ftmp_N[N] + 1;
+			}
+		}
+	}
+
+	//Q_I,tmp_N = Q_0_N-1 \ Q_F,tmp_N
+	for (int n = 0; n <= N - 1; n++) {
+		flag = 1;
+		for (int m = 0; m <= Q_Ftmp_N[N]; m++) {
+			if (Q_0_Nminus1[n] == Q_Ftmp_N[m]) {
+				flag = 0;
+				break;
+			}
+		}
+		if (flag) {
+			Q_Itmp_N[Q_Itmp_N[N] + 1] = Q_0_Nminus1[n];
+			Q_Itmp_N[N]++;
+		}
+	}
+
+	//Q_I_N comprises (K+n_PC) most reliable bit indices in Q_I,tmp_N
+	for (int n = 0; n <= (K + n_PC) - 1; n++) {
+		ind = Q_Itmp_N[N] + n - ((K + n_PC) - 1);
+		Q_I_N[n] = Q_Itmp_N[ind];
+	}
+
+	//Q_F_N = Q_0_N-1 \ Q_I_N
+	for (int n = 0; n <= N - 1; n++) {
+		flag = 1;
+		for (int m = 0; m <= (K + n_PC) - 1; m++) {
+			if (Q_0_Nminus1[n] == Q_I_N[m]) {
+				flag = 0;
+				break;
+			}
+		}
+		if (flag) {
+			Q_F_N[Q_F_N[N] + 1] = Q_0_Nminus1[n];
+			Q_F_N[N]++;
+		}
+	}
+
+	//Information Bit Pattern
+	for (int n = 0; n <= N - 1; n++) {
+		ibp[n] = 0;
+
+		for (int m = 0; m <= (K + n_PC) - 1; m++) {
+			if (n == Q_I_N[m]) {
+				ibp[n] = 1;
+				break;
+			}
+		}
+	}
+
+	free(Q_Ftmp_N);
+	free(Q_Itmp_N);
+}
+
+void nr_polar_info_bit_extraction(uint8_t *input, uint8_t *output, uint8_t *pattern, uint16_t size) {
+	uint16_t j = 0;
+	for (int i = 0; i < size; i++) {
+		if (pattern[i] > 0) {
+			output[j] = input[i];
+			j++;
+		}
+	}
+}

openair1/PHY/CODING/nrPolar_tools/nr_polar_interleave.c

+#include "PHY/CODING/nrPolar_tools/nr_polar_defs.h"
+
+void nr_polar_interleaving_pattern(uint16_t K, uint8_t I_IL, uint16_t *PI_k_){
+	uint8_t K_IL_max=164, k=0;
+	uint8_t interleaving_pattern_table[164] = {0, 2, 4, 7, 9, 14, 19, 20, 24, 25, 26, 28, 31, 34,
+			42, 45, 49, 50, 51, 53, 54, 56, 58, 59, 61, 62, 65, 66,
+			67, 69, 70, 71, 72, 76, 77, 81, 82, 83, 87, 88, 89, 91,
+			93, 95, 98, 101, 104, 106, 108, 110, 111, 113, 115, 118, 119, 120,
+			122, 123, 126, 127, 129, 132, 134, 138, 139, 140, 1, 3, 5, 8,
+			10, 15, 21, 27, 29, 32, 35, 43, 46, 52, 55, 57, 60, 63,
+			68, 73, 78, 84, 90, 92, 94, 96, 99, 102, 105, 107, 109, 112,
+			114, 116, 121, 124, 128, 130, 133, 135, 141, 6, 11, 16, 22, 30,
+			33, 36, 44, 47, 64, 74, 79, 85, 97, 100, 103, 117, 125, 131,
+			136, 142, 12, 17, 23, 37, 48, 75, 80, 86, 137, 143, 13, 18,
+			38, 144, 39, 145, 40, 146, 41, 147, 148, 149, 150, 151, 152, 153,
+			154, 155, 156, 157, 158, 159, 160, 161, 162, 163};
+	
+	if (I_IL == 0){
+		for (; k<= K-1; k++)
+			PI_k_[k] = k;
+	} else {
+		for (int m=0; m<= (K_IL_max-1); m++){
+			if (interleaving_pattern_table[m] >= (K_IL_max-K)) {
+				PI_k_[k] = interleaving_pattern_table[m]-(K_IL_max-K);
+				k++;
+			}
+		}
+	}
+}
+
+void nr_polar_interleaver(uint8_t *input, uint8_t *output, uint16_t *pattern, uint16_t size) {
+	for (int i=0; i<size; i++) output[i]=input[pattern[i]];
+}
+
+void nr_polar_deinterleaver(uint8_t *input, uint8_t *output, uint16_t *pattern, uint16_t size) {
+	for (int i=0; i<size; i++) output[pattern[i]]=input[i];
+}

openair1/PHY/CODING/nrPolar_tools/nr_polar_kernal_operation.c

+#include <stdio.h>
+#include <stdlib.h>
+#include <math.h>
+#include <stdint.h>
+
+void nr_polar_kernel_operation(uint8_t *u, uint8_t *d, uint16_t N)
+{
+    // Martino's algorithm to avoid multiplication for the generating matrix
+
+    int i,j;
+    printf("\nd = ");
+	for(i=0; i<N; i++)
+    {
+        d[i]=0;
+        for(j=0; j<N; j++)
+        {
+            d[i]=d[i]+(( (j-i)& i )==0)*u[j];
+        }
+        d[i]=d[i]%2;
+
+        printf("%i", d[i]);
+    }
+}

openair1/PHY/CODING/nrPolar_tools/nr_polar_matrix_and_array.c

+#include "PHY/CODING/nrPolar_tools/nr_polar_defs.h"
+
+void nr_matrix_multiplication_uint8_t_1D_uint8_t_2D(uint8_t *matrix1, uint8_t **matrix2,
+		uint8_t *output, uint16_t row, uint16_t col) {
+
+	for (uint16_t i = 0; i < col; i++) {
+		output[i] = 0;
+		for (uint16_t j = 0; j < row; j++) {
+			output[i] += matrix1[j] * matrix2[j][i];
+		}
+	}
+}
+
+uint8_t ***nr_alloc_uint8_t_3D_array(uint16_t xlen, uint16_t ylen, uint16_t zlen) {
+	uint8_t ***output;
+	int i, j;
+
+	if ((output = malloc(xlen * sizeof(*output))) == NULL) {
+		perror("[nr_alloc_uint8_t_3D_array] Problem at 1D allocation");
+		return NULL;
+	}
+	for (i = 0; i < xlen; i++)
+		output[i] = NULL;
+
+
+	for (i = 0; i < xlen; i++)
+		if ((output[i] = malloc(ylen * sizeof *output[i])) == NULL) {
+			perror("[nr_alloc_uint8_t_3D_array] Problem at 2D allocation");
+			nr_free_uint8_t_3D_array(output, xlen, ylen);
+			return NULL;
+		}
+	for (i = 0; i < xlen; i++)
+		for (j = 0; j < ylen; j++)
+			output[i][j] = NULL;
+
+
+	for (i = 0; i < xlen; i++)
+		for (j = 0; j < ylen; j++)
+			if ((output[i][j] = malloc(zlen * sizeof *output[i][j])) == NULL) {
+				perror("[nr_alloc_uint8_t_3D_array] Problem at 3D allocation");
+				nr_free_uint8_t_3D_array(output, xlen, ylen);
+				return NULL;
+			}
+
+	return output;
+}
+
+double ***nr_alloc_double_3D_array(uint16_t xlen, uint16_t ylen, uint16_t zlen) {
+	double ***output;
+	int i, j;
+
+	if ((output = malloc(xlen * sizeof(*output))) == NULL) {
+		perror("[nr_alloc_double_3D_array] Problem at 1D allocation");
+		return NULL;
+	}
+	for (i = 0; i < xlen; i++)
+		output[i] = NULL;
+
+
+	for (i = 0; i < xlen; i++)
+		if ((output[i] = malloc(ylen * sizeof *output[i])) == NULL) {
+			perror("[nr_alloc_double_3D_array] Problem at 2D allocation");
+			nr_free_double_3D_array(output, xlen, ylen);
+			return NULL;
+		}
+	for (i = 0; i < xlen; i++)
+		for (j = 0; j < ylen; j++)
+			output[i][j] = NULL;
+
+
+	for (i = 0; i < xlen; i++)
+		for (j = 0; j < ylen; j++)
+			if ((output[i][j] = malloc(zlen * sizeof *output[i][j])) == NULL) {
+				perror("[nr_alloc_double_3D_array] Problem at 3D allocation");
+				nr_free_double_3D_array(output, xlen, ylen);
+				return NULL;
+			}
+
+	return output;
+}
+
+uint8_t **nr_alloc_uint8_t_2D_array(uint16_t xlen, uint16_t ylen) {
+	uint8_t **output;
+	int i, j;
+
+	if ((output = malloc(xlen * sizeof(*output))) == NULL) {
+		perror("[nr_alloc_uint8_t_2D_array] Problem at 1D allocation");
+		return NULL;
+	}
+	for (i = 0; i < xlen; i++)
+		output[i] = NULL;
+
+
+	for (i = 0; i < xlen; i++)
+		if ((output[i] = malloc(ylen * sizeof *output[i])) == NULL) {
+			perror("[nr_alloc_uint8_t_2D_array] Problem at 2D allocation");
+			nr_free_uint8_t_2D_array(output, xlen);
+			return NULL;
+		}
+	for (i = 0; i < xlen; i++)
+		for (j = 0; j < ylen; j++)
+			output[i][j] = 0;
+
+	return output;
+}
+
+void nr_free_uint8_t_3D_array(uint8_t ***input, uint16_t xlen, uint16_t ylen) {
+	int i, j;
+
+	for (i = 0; i < xlen; i++) {
+		for (j = 0; j < ylen; j++) {
+			free(input[i][j]);
+		}
+		free(input[i]);
+	}
+	free(input);
+}
+
+void nr_free_uint8_t_2D_array(uint8_t **input, uint16_t xlen) {
+	for (int i = 0; i < xlen; i++) free(input[i]);
+	free(input);
+}
+
+void nr_free_double_3D_array(double ***input, uint16_t xlen, uint16_t ylen) {
+	int i, j;
+
+	for (i = 0; i < xlen; i++) {
+		for (j = 0; j < ylen; j++) {
+			free(input[i][j]);
+		}
+		free(input[i]);
+	}
+	free(input);
+}
+
+// Modified Bubble Sort.
+void nr_sort_asc_double_1D_array_ind(double *matrix, uint8_t *ind, uint8_t len) {
+	uint8_t swaps;
+	double temp;
+	uint8_t tempInd;
+
+	for (uint8_t i = 0; i < len; i++) {
+		swaps = 0;
+		for (uint8_t j = 0; j < (len - i) - 1; j++) {
+			if (matrix[j] > matrix[j + 1]) {
+				temp = matrix[j];
+				matrix[j] = matrix[j + 1];
+				matrix[j + 1] = temp;
+
+				tempInd = ind[j];
+				ind[j] = ind[j + 1];
+				ind[j + 1] = tempInd;
+
+				swaps++;
+			}
+		}
+		if (swaps == 0)
+			break;
+	}
+}

openair1/PHY/CODING/nrPolar_tools/nr_polar_output_length.c

+#include <math.h>
+#include "PHY/CODING/nrPolar_tools/nr_polar_defs.h"
+
+uint32_t nr_polar_output_length(uint16_t K, uint16_t E, uint8_t n_max){
+	uint8_t n_1, n_2, n_min=5, n;
+	uint32_t polar_code_output_length;
+	double R_min=1.0/8;
+	
+	if ( (E <= (9.0/8)*pow(2,ceil(log2(E))-1)) && (K/E < 9.0/16) ) {
+		n_1 = ceil(log2(E))-1;		
+	} else {
+		n_1 = ceil(log2(E));
+	}
+	
+	n_2 = ceil(log2(K/R_min));
+	
+	n=n_max;
+	if (n>n_1) n=n_1;
+	if (n>n_2) n=n_2;
+	if (n<n_min) n=n_min;
+	
+	polar_code_output_length = (uint32_t) pow(2.0,n);
+	
+	return polar_code_output_length;
+}

openair1/PHY/CODING/nrPolar_tools/nr_polar_pbch_defs.h

+/*
+ * Defines the constant variables for polar coding of the PBCH.
+ */
+
+#ifndef __NR_POLAR_PBCH_DEFS__H__
+#define __NR_POLAR_PBCH_DEFS__H__
+
+
+#define NR_POLAR_PBCH_PAYLOAD_BITS 32 //uint16_t
+#define NR_POLAR_PBCH_CRC_PARITY_BITS 24
+#define NR_POLAR_PBCH_CRC_ERROR_CORRECTION_BITS 3
+//Assumed 3 by 3GPP when NR_POLAR_PBCH_L>8 to meet false alarm rate requirements.
+
+//Ref. 38-212 v15.0.1, Section 7.1.4: Channel Coding
+#define NR_POLAR_PBCH_N_MAX 9   //uint8_t
+#define NR_POLAR_PBCH_I_IL 1    //uint8_t
+#define NR_POLAR_PBCH_N_PC 0    //uint8_t
+#define NR_POLAR_PBCH_N_PC_WM 0 //uint8_t
+//#define NR_POLAR_PBCH_N 512     //uint16_t
+
+//Ref. 38-212 v15.0.1, Section 7.1.5: Rate Matching
+#define NR_POLAR_PBCH_I_BIL 0 //uint8_t
+#define NR_POLAR_PBCH_E 864   //uint16_t
+
+//#define NR_POLAR_PBCH_L 5 //uint8_t
+#define NR_POLAR_PBCH_PATH_METRIC_APPROXIMATION 0 //uint8_t; 0 --> eq. (8a) and (11b), 1 --> eq. (9) and (12)
+
+/*
+ * TEST CODE
+ */
+//#define DEBUG_POLAR
+// Usage in code:
+//#ifdef DEBUG_POLAR
+//...
+//#endif
+
+//unsigned int testPayload0=0x00000000, testPayload1=0xffffffff; //payload1=~payload0;
+//unsigned int testPayload2=0xa5a5a5a5; //testPayload3=0xb3f02c82;
+
+//double testReceivedPayload3[NR_POLAR_PBCH_E] = {-1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1, -1, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, -1, -1, -1, -1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, 1, -1, -1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, 1, 1, -1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, -1, -1, -1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, 1, -1, -1, 1, -1, 1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, -1, -1, -1, -1, 1, 1, 1, 1, 1, -1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, 1, 1, -1, 1, -1, 1, -1, 1, -1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, -1, 1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, 1, 1, 1, 1, 1, 1, -1, 1, 1, -1, 1, 1, 1, -1, -1, 1, 1, 1, 1, -1, 1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, -1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, 1, -1, -1, -1, -1, -1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, -1, 1, 1, 1, -1, -1, -1, 1, 1, 1, -1, -1, -1, 1, -1, -1, 1, 1, 1, -1, 1, -1, -1, 1, -1, 1, -1, 1, -1, 1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, 1, 1, -1, -1, 1, 1, -1, 1, 1, -1, -1, 1, 1, -1, -1};
+
+#endif

openair1/PHY/CODING/nrPolar_tools/nr_polar_pucch_defs.h

+/*
+ * Defines the constant variables for polar coding of the PUCCH.
+ */
+
+#ifndef __NR_POLAR_PUCCH_DEFS__H__
+#define __NR_POLAR_PUCCH_DEFS__H__
+
+#define NR_POLAR_PUCCH_PAYLOAD_BITS 16
+
+//Ref. 38-212 v15.0.1
+#define NR_POLAR_PUCCH_N_MAX 10   //uint8_t <------
+#define NR_POLAR_PUCCH_I_IL 1    //uint8_t <--- interleaving: if 0 no interleaving
+#define NR_POLAR_PUCCH_N_PC 3    //uint8_t <-- or zero ??
+#define NR_POLAR_PUCCH_N_PC_WM 0 //uint8_t
+//#define NR_POLAR_PUCCH_N 512     //uint16_t
+
+//Ref. 38-212 v15.0.1, Section 7.1.5: Rate Matching
+#define NR_POLAR_PUCCH_I_BIL 0 //uint8_t
+#define NR_POLAR_PUCCH_E 864   //uint16_t
+
+
+/*
+ * TEST CODE
+ */
+//unsigned int testPayload0=0x00000000, testPayload1=0xffffffff; //payload1=~payload0;
+//unsigned int testPayload2=0xa5a5a5a5, testPayload3=0xb3f02c82;
+
+#endif

openair1/PHY/CODING/nrPolar_tools/nr_polar_rate_match.c

+#include <math.h>
+#include "PHY/CODING/nrPolar_tools/nr_polar_defs.h"
+
+void nr_polar_rate_matching_pattern(uint16_t *rmp, uint16_t *J, uint8_t *P_i_, uint16_t K, uint16_t N, uint16_t E){
+	
+	uint8_t i;
+	uint16_t *d, *y, ind;
+	d = (uint16_t *)malloc(sizeof(uint16_t) * N);
+	y = (uint16_t *)malloc(sizeof(uint16_t) * N);
+	
+	for (int m=0; m<=N-1; m++) d[m]=m;
+	
+	for (int m=0; m<=N-1; m++){
+		i=floor((32*m)/N);
+		J[m] = (P_i_[i]*(N/32)) + (m%(N/32));
+		y[m] = d[J[m]];
+	}
+	
+	if (E>=N) { //repetition
+		for (int k=0; k<=E-1; k++) {
+			ind = (k%N);
+			rmp[k]=y[ind];
+		}
+	} else {
+		if ( (K/(double)E) <= (7.0/16) ) { //puncturing
+			for (int k=0; k<=E-1; k++) {
+				rmp[k]=y[k+N-E];
+			}
+		} else { //shortening
+			for (int k=0; k<=E-1; k++) {
+				rmp[k]=y[k];
+			}
+		}	
+	}	
+	
+	free(d);
+	free(y);
+}
+
+
+void nr_polar_rate_matching(double *input, double *output, uint16_t *rmp, uint16_t K, uint16_t N, uint16_t E){
+
+	if (E>=N) { //repetition
+		for (int i=0; i<=N-1; i++) output[i]=0;
+		for (int i=0; i<=E-1; i++){
+			output[rmp[i]]+=input[i];
+		}
+	} else {
+		if ( (K/(double)E) <= (7.0/16) ) { //puncturing
+			for (int i=0; i<=N-1; i++) output[i]=0;
+		} else { //shortening
+			for (int i=0; i<=N-1; i++) output[i]=INFINITY;
+		}
+
+		for (int i=0; i<=E-1; i++){
+			output[rmp[i]]=input[i];
+		}
+	}
+
+}
+
+void nr_polar_rate_matcher(uint8_t *input, unsigned char *output, uint16_t *pattern, uint16_t size) {
+	for (int i=0; i<size; i++) output[i]=input[pattern[i]];
+}