Code covered by the BSD License

### Highlights from EXIT chart computation

• EXITComputes the A priori Mutual Information assuming a Gaussian distribution
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# EXIT chart computation

### Bogdan Cristea (view profile)

26 Aug 2009 (Updated )

Matlab class implementing several methods for the computation of EXIT charts.

EXIT
```% Computes the A priori Mutual Information assuming a Gaussian distribution
%of the a priori information and the Extrinsic Mutual Information between
%the emitted bits and their extrinsic information
%
% Description:
% - the a priori mutual information is computed using relation (14)
% - the extrinsic mutual information is computed by estimating first the
%conditional Probability Density Functions (PDF), given the emitted bits,
%and then numerically integrating according to relation (19)
%
% Reference:
% Stephan ten Brink, ''Convergence behavior of iteratively decoded parallel
% concatenated codes,`` IEEE Transactions on Communications, oct. 2001
%
% Usage example:
% exit = EXIT;%EXIT chart object
% set ( exit, 'sigma2A', sigma2A(en) );%set the variance of the a priori mutual information (sigma2A)
% apriori_mutual_info = exit.apriori_mutual_info ();%generate a priori mutual info
% [extrinsic_coded extrinsic_data] = C_SISOrsc ( Li, exit.generate_apriori_info ( bits ), bin_gen, 0, map_metric );%MAP algorithm implementation (the EXIT object is used to generate a priori info)
% extrinsic_mutual_info = exit.extrinsic_mutual_info ( extrinsic_data, bits );%compute extrinsic mutual information
% plot ( apriori_mutual_info, extrinsic_mutual_info )%plot transfer characteristic (a second extrinsic mutual info is needed in order to obtain the EXIT chart)

classdef EXIT < hgsetget
properties
sigma2A = 0;
integration_interval_limit = 100;
subinterval_nb = 100;
end
methods
%Sets the variance of the a priori information
%Call syntax: set ( exit, 'sigma2A', sigma2A(en) );
function obj = set.sigma2A ( obj, in_sigma2A )
obj.sigma2A = in_sigma2A;
end
%Sets the integration interval limit for mutual a apriori info
function obj = set.integration_interval_limit ( obj, in_lim )
obj.integration_interval_limit = in_lim;
end
%Sets the number of subintervals used for pdf estimation
function obj = set.subinterval_nb ( obj, in_subint )
obj.subinterval_nb = in_subint;
end
% Computes a priori information using the Gaussian approximation
function IA = apriori_mutual_info ( obj )
IA = 1 - quad ( @obj.gaussian_fct, ...
-obj.integration_interval_limit, ...
obj.integration_interval_limit );
end
% Generates a priori information assuming a Gaussian distribution
%of the a priori information. The BPSK mapping is done as follows:
%0 -> +1 and 1 -> -1
% The input is bits - a vector of zeros and ones
function out = generate_apriori_info ( obj, bits )
out = (obj.sigma2A/2)*(2*bits-1)+...
sqrt(obj.sigma2A)*randn(1, length(bits));
end
% Computes the extrinsic mutual information
% The inputs are: obs - extrinsic information obtained from the
%SISO module output
%                 cond - emitted bits corresponding to the
%extrinsic information
function IE = extrinsic_mutual_info ( obj, obs, cond )
%compute endges for histogram computation
min_obs = min ( obs );
max_obs = max ( obs );
edges = min_obs:((max_obs-min_obs)/obj.subinterval_nb):max_obs;

%conditional PDF knowing that a bit of 0 was emitted
cond_obs = obs(cond == 0);
nb_values_subinterval = histc ( cond_obs, edges );%count values
left_pdf = nb_values_subinterval(1:(end-1))./ ...
length(cond_obs);%the pdf is computed without taking into
%account the subinterval length (step)
left_int = find ( left_pdf ~= 0 );%integration interval for the left PDF

%conditional PDF knowing that a bit of 1 was emitted
cond_obs = obs(cond == 1);
nb_values_subinterval = histc ( cond_obs, edges );%count values
right_pdf = nb_values_subinterval(1:(end-1))./ ...
length(cond_obs);
right_int = find ( right_pdf ~= 0 );%integration interval for the right PDF

%mutual extrinsic information
left_half = left_pdf(left_int).*log2(2.0*left_pdf(left_int)./ ...
(left_pdf(left_int)+right_pdf(left_int)));
right_half = right_pdf(right_int).*log2(2.0*right_pdf(right_int)./ ...
(left_pdf(right_int)+right_pdf(right_int)));
%numerical integration without taking into account the interval
%length (see conditional PDF computation)
IE = 0;
if ~isempty ( left_half )
IE = IE + 0.5*(sum(left_half)-0.5*(left_half(1)+left_half(end)));
end
if ~isempty ( right_half )
IE = IE + 0.5*(sum(right_half)-0.5*(right_half(1)+right_half(end)));
end
end
%Gaussian function used to generate the a priori information
function y = gaussian_fct ( obj, x )
y = (1/sqrt(obj.sigma2A*2*pi))* ...
exp(-((x-(obj.sigma2A/2.0)).^2)/(2.0*obj.sigma2A)).* ...
log2(1+exp(-x));
end
end
end```