CCS - Channel Capacity and Coding - Channel Coding - Performance of Linear Block Codes

 

Performance of Linear Block Codes

Linear block codes can be decoded using either soft-decision decoding or hard-decision
decoding. In a hard-decision decoding scheme, first a bit-by-bit decision is made on the
components of the codeword, and then, with a minimum Hamming distance criterion,
the decoding is performed. The performance of this decoding scheme depends on the
distance structure of the code, but a tight upper bound, particularly at high values of
the SNR, can be obtained in terms of the minimum distance of the code.

 

 

 

 

 

 

 

 

 

 

 

 

 

Matlab Coding

 

 

 

 

 

 

% MATLAB script for Illustrative Problem 10.11.
echo on
gamma_b_db=[-4:1:14];
gamma_b=10.^(gamma_b_db/10);
qq=q(sqrt(0.733.*gamma_b));
p_err=2047*qq.^2.*(3-2.*qq);  
semilogy(gamma_b,p_err)
ylabel('Pe')
xlabel('dB')

 

 

 

 

 

 

 

 

 

 

In comparing these error rate expressions, we observe that

antipodal signaling is 3 dB better than orthogonal signaling.

% MATLAB script for Illustrative Problem 10.12.
[p_err_ha,gamma_b]=p_e_hd_a(7,13,11,15,3);
[p_err_ho,gamma_b]=p_e_hd_o(7,13,11,15,3);
[p_err_so,gamma_b]=p_e_sd_o(7,13,11,15,3);
[p_err_sa,gamma_b]=p_e_sd_a(7,13,11,15,3);
semilogy(gamma_b,p_err_sa,gamma_b,p_err_so,gamma_b,p_err_ha,gamma_b,p_err_ho)



function [p_err,gamma_db]=p_e_sd_o(gamma_db_l,gamma_db_h,k,n,d_min)
% p_e_sd_o.m     Matlab function for computing error probability in
%                soft-decision decoding of a linear block code
%                when orthogonal signaling is used.
%          [p_err,gamma_db]=p_e_sd_o(gamma_db_l,gamma_db_h,k,n,d_min)
%          gamma_db_l=lower E_b/N_0
%          gamma_db_h=higher E_b/N_0
%          k=number of information bits in the code
%          n=code block length
%          d_min=minimum distance of the code

gamma_db=[gamma_db_l:(gamma_db_h-gamma_db_l)/20:gamma_db_h];
gamma_b=10.^(gamma_db/10);
R_c=k/n;
p_err=(2^k-1).*q(sqrt(d_min.*R_c.*gamma_b));



function [p_err,gamma_db]=p_e_hd_o(gamma_db_l,gamma_db_h,k,n,d_min)
% p_e_hd_o.m     Matlab function for computing error probability in
%                hard-decision decoding of a linear block code
%                when orthogonal signaling is used.
%          [p_err,gamma_db]=p_e_hd_o(gamma_db_l,gamma_db_h,k,n,d_min)
%          gamma_db_l=lower E_b/N_0
%          gamma_db_h=higher E_b/N_0
%         k=number of information bits in the code
%          n=code block length
%          d_min=minimum distance of the code

gamma_db=[gamma_db_l:(gamma_db_h-gamma_db_l)/20:gamma_db_h];
gamma_b=10.^(gamma_db/10);
R_c=k/n;
p_b=q(sqrt(R_c.*gamma_b));
p_err=(2^k-1).*(4*p_b.*(1-p_b)).^(d_min/2);

 

Reference,

　　1. <<Contemporary Communication System using MATLAB>> - John G. Proakis