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

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

In comparing these error rate expressions, we observe that

antipodal signaling is 3 dB better than orthogonal signaling.

 1 % MATLAB script for Illustrative Problem 10.12.
 2 [p_err_ha,gamma_b]=p_e_hd_a(7,13,11,15,3);
 3 [p_err_ho,gamma_b]=p_e_hd_o(7,13,11,15,3);
 4 [p_err_so,gamma_b]=p_e_sd_o(7,13,11,15,3);
 5 [p_err_sa,gamma_b]=p_e_sd_a(7,13,11,15,3);
 6 semilogy(gamma_b,p_err_sa,gamma_b,p_err_so,gamma_b,p_err_ha,gamma_b,p_err_ho)
 7 
 8 
 9 
10 function [p_err,gamma_db]=p_e_sd_o(gamma_db_l,gamma_db_h,k,n,d_min)
11 % p_e_sd_o.m     Matlab function for computing error probability in
12 %                soft-decision decoding of a linear block code
13 %                when orthogonal signaling is used.
14 %          [p_err,gamma_db]=p_e_sd_o(gamma_db_l,gamma_db_h,k,n,d_min)
15 %          gamma_db_l=lower E_b/N_0
16 %          gamma_db_h=higher E_b/N_0
17 %          k=number of information bits in the code
18 %          n=code block length
19 %          d_min=minimum distance of the code
20 
21 gamma_db=[gamma_db_l:(gamma_db_h-gamma_db_l)/20:gamma_db_h];
22 gamma_b=10.^(gamma_db/10);
23 R_c=k/n;
24 p_err=(2^k-1).*q(sqrt(d_min.*R_c.*gamma_b));
25 
26 
27 
28 function [p_err,gamma_db]=p_e_hd_o(gamma_db_l,gamma_db_h,k,n,d_min)
29 % p_e_hd_o.m     Matlab function for computing error probability in
30 %                hard-decision decoding of a linear block code
31 %                when orthogonal signaling is used.
32 %          [p_err,gamma_db]=p_e_hd_o(gamma_db_l,gamma_db_h,k,n,d_min)
33 %          gamma_db_l=lower E_b/N_0
34 %          gamma_db_h=higher E_b/N_0
35 %         k=number of information bits in the code
36 %          n=code block length
37 %          d_min=minimum distance of the code
38 
39 gamma_db=[gamma_db_l:(gamma_db_h-gamma_db_l)/20:gamma_db_h];
40 gamma_b=10.^(gamma_db/10);
41 R_c=k/n;
42 p_b=q(sqrt(R_c.*gamma_b));
43 p_err=(2^k-1).*(4*p_b.*(1-p_b)).^(d_min/2);