EXIT chart of PCCCs

This program computes the EXtrinsic Information Transfer (EXIT) chart for Parallel Concatenated Convolutional Codes (PCCCs) of coding rate 1/3. Actually the Transfer Characteristics (TCs) of the two SISO RSC modules used in the turbo decoder are computed at a given Signal to Noise Ratio (SNR).

Reference: S. ten Brink, ''Convergence behavior of iteratively decoded parallel concatenated codes,`` IEEE Transactions on Communications, vol. 49, pp. 1727-1737, Oct. 2001

#include "itpp/itcomm.h"

using namespace itpp;
using std::cout;
using std::endl;
using std::string;

int main(void)
{
  //general parameters
  vec sigmaA = "0.01:0.1:7";//standard deviation (sqrt(variance)) of the mutual a priori information
  double threshold_value = 50;
  string map_metric = "maxlogMAP";
  ivec gen = "07 05";//octal form
  int constraint_length = 3;
  int nb_blocks_lim = 10;
  int perm_len = int(itpp::pow10(5.0));//total number of bits in a block (with tail)
  double EbN0_dB = 0.6;
  double R = 1.0 / 3.0;//coding rate of PCCC
  double Ec = 1.0;//coded bit energy

  //other parameters
  vec sigma2A = sqr(sigmaA);
  int sigma2A_len = sigma2A.length();
  int nb_bits = perm_len - (constraint_length - 1);//number of bits in a block (without tail)
  double sigma2 = (0.5 * Ec / R) * pow(inv_dB(EbN0_dB), -1.0);//N0/2
  double Lc = -2 / sigma2;//normalisation factor for intrinsic information (take into account the BPSK modulation)
  bvec bits(nb_bits);
  bvec tail;
  bvec bits_tail(perm_len);
  bmat parity_bits;
  int coded_bits_len = 2 * perm_len;
  bvec coded_bits(coded_bits_len);
  vec mod_bits(coded_bits_len);
  vec rec_sig(coded_bits_len);
  vec intrinsic_coded(coded_bits_len);
  vec intrinsic_coded_p(2*nb_bits);
  intrinsic_coded_p.zeros();
  vec apriori_data(perm_len);
  vec extrinsic_coded;
  vec extrinsic_data;
  vec apriori_mutual_info(sigma2A_len);
  vec extrinsic_mutual_info(sigma2A_len);
  vec extrinsic_mutual_info_p(sigma2A_len);
  extrinsic_mutual_info.zeros();
  extrinsic_mutual_info_p.zeros();
  register int en, n, nb_blocks;

  //Recursive Systematic Convolutional Code
  Rec_Syst_Conv_Code rsc;
  rsc.set_generator_polynomials(gen, constraint_length);//initial state should be the zero state

  //BPSK modulator
  BPSK bpsk;

  //AWGN channel
  AWGN_Channel channel;
  channel.set_noise(sigma2);

  //SISO module
  SISO siso;
  siso.set_generators(gen, constraint_length);
  siso.set_map_metric(map_metric);

  //EXIT chart
  EXIT exit;

  //Randomize generators
  RNG_randomize();

  //main loop
  for (en = 0;en < sigma2A_len;en++) {
    apriori_mutual_info(en) = exit.apriori_mutual_info(sigma2A(en));//a priori mutual info
    cout << "I_A = " << apriori_mutual_info(en) << endl;
    for (nb_blocks = 0;nb_blocks < nb_blocks_lim;nb_blocks++) {
      //bits generation
      bits = randb(nb_bits);

      //RSC code
      rsc.encode_tail(bits, tail, parity_bits);//tail is added

      //form coder output
      bits_tail = concat(bits, tail);
      for (n = 0;n < perm_len;n++) {
        coded_bits(2*n) = bits_tail(n);//systematic output
        coded_bits(2*n + 1) = parity_bits(n, 0);//parity output
      }

      //BPSK modulation (1->-1,0->+1)
      mod_bits = bpsk.modulate_bits(coded_bits);

      //AWGN channel
      rec_sig = channel(mod_bits);

      //first SISO RSC module  (tail is added)
      //intrinsic info. of coded bits
      intrinsic_coded = Lc * rec_sig;

      //a priori info. of data bits
      apriori_data = exit.generate_apriori_info(bits_tail);

      //SISO RSC module
      siso.rsc(extrinsic_coded, extrinsic_data, intrinsic_coded, apriori_data, true);

      //threshold
      extrinsic_data = SISO::threshold(extrinsic_data, threshold_value);

      //extrinsic mutual info
      extrinsic_mutual_info(en) += exit.extrinsic_mutual_info(extrinsic_data.left(nb_bits), bits);

      //second SISO RSC module (no tail added)
      //intrinsic info. of coded bits
      for (n = 0;n < nb_bits;n++)
        intrinsic_coded_p(2*n + 1) = Lc * rec_sig(2 * n + 1);//parity bits only

      //a priori info. of data bits
      apriori_data = exit.generate_apriori_info(bits);

      //SISO RSC module
      siso.rsc(extrinsic_coded, extrinsic_data, intrinsic_coded_p, apriori_data, false);

      //threshold
      extrinsic_data = SISO::threshold(extrinsic_data, threshold_value);

      //extrinsic mutual info
      extrinsic_mutual_info_p(en) += exit.extrinsic_mutual_info(extrinsic_data, bits);
    }//end blocks (while loop)

    //mean extrinsic mutual info over all blocks
    extrinsic_mutual_info(en) /= nb_blocks_lim;
    extrinsic_mutual_info_p(en) /= nb_blocks_lim;
  }

  it_file ff("exit_pccc.it");
  ff << Name("IA") << apriori_mutual_info;
  ff << Name("IE") << extrinsic_mutual_info;
  ff << Name("IE_p") << extrinsic_mutual_info_p;
  ff << Name("EbN0_dB") << EbN0_dB;
  ff << Name("gen") << gen;
  ff << Name("R") << R;
  ff << Name("perm_len") << perm_len;
  ff << Name("nb_blocks_lim") << nb_blocks_lim;
  ff.close();

  return 0;
}

When you run this program, the results (mutual a priori and extrinsic information, EbN0_dB, etc.) are saved into exit_pccc.it file. Using the following MATLAB script

clear all
itload('exit_pccc.it')
plot(IA, IE, 'LineWidth', 3)
hold on
plot(IE_p, IA, 'LineWidth', 3)
xlabel('I_A^{(up)}, I_E^{(low)}')
ylabel('I_E^{(up)}, I_A^{(low)}')
grid on
title(['E_b/N_0 = ' num2str(EbN0_dB) ' dB'])

the EXIT chart can be displayed.