exit.cpp

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#include <itpp/comm/exit.h>
#include <itpp/stat/histogram.h> //histogram class for mutual information computation
#include <itpp/base/itcompat.h>

namespace itpp
{
double EXIT::Gaussian_Fct::operator()(double x) const
{
  return (1.0/std::sqrt(_sigma*itpp::m_2pi))*std::exp(-itpp::sqr(x-(_sigma/2.0))/(2.0*_sigma))*::log2(1+std::exp(-x));
}

double EXIT::extrinsic_mutual_info(const itpp::vec &obs, const itpp::bvec &cond, const int &N)
{
    //initialize histogram
    itpp::Histogram<double> hist(itpp::min(obs), itpp::max(obs), N);//common definition interval for both PDFs

    //conditional PDF knowing that a bit of 0 was emitted
    itpp::ivec idx = itpp::find(cond==itpp::bin(0));
    itpp::vec cond_obs = obs(idx);
    hist.reset();//start counting
    hist.update(cond_obs);
    itpp::vec left_pdf = hist.get_pdf();//the pdf is computed without taking into account the interval length (step)
    itpp::ivec left_int = itpp::find(left_pdf!=0);//integration interval for the left PDF

    //conditional PDF knowing that a bit of 1 was emitted
    idx = itpp::find(cond==itpp::bin(1));
    cond_obs = obs(idx);
    hist.reset();//restart counting
    hist.update(cond_obs);
    itpp::vec right_pdf = hist.get_pdf();
    itpp::ivec right_int = itpp::find(right_pdf!=0);//integration interval for the right PDF

    //mutual extrinsic information
    itpp::vec left_half = itpp::elem_mult(left_pdf(left_int), itpp::log2(itpp::elem_div(2.0*left_pdf(left_int), left_pdf(left_int)+right_pdf(left_int))));
    double IE = itpp::sum(left_half)-0.5*(left_half(0)+left_half(left_half.length()-1));//numerical integration without taking into account the inteval length (see conditional PDF computation)
    itpp::vec right_half = itpp::elem_mult(right_pdf(right_int), itpp::log2(itpp::elem_div(2.0*right_pdf(right_int), left_pdf(right_int)+right_pdf(right_int))));
    IE += itpp::sum(right_half)-0.5*(right_half(0)+right_half(right_half.length()-1));//numerical integration
    IE *= 0.5;

    return IE;
}

}//namespace itpp