1.完整项目描述和程序获取
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2.部分仿真图预览
3.算法概述
汉明码是一种性能良好的码，它是在纠错编码的实践中较早发现的一类具有纠单个错误能力的纠错码，在通信和计算机工程中都有应用。例如：在“计算机组成原理”课程中，我们知道当计算机存储或移动数据时，可能会产生数据位错误，这时可以利用汉明码来检测并纠错。简单的说，汉明码是一个错误校验码码集，由Bell实验室的R.W.Hamming发明，因此定名为汉明码。如果对汉明码作进一步推广，就得出了能纠正多个错误的纠错码，其中最典型的是BCH码，而且汉明码是只纠1bit错误的BCH码，可将它们都归纳到循环码中。
4.部分源码
clc;
clear;
close all;
warning off;
addpath(genpath(pwd));
%% Demonstration of Soft-Hamming-Decoding based on Sphere-Decoding
Kc=5; %Number of Parity bits
Nframes=3; %Number of Frames
M=3; %maximium bit error number M (Size of Sphere)
ExtHammCode=1; % 1 for extended Hamming-Code
%K_loop for more runs at higher SNR
SNRdB=0:1:7;
K_loop=round((SNRdB-min(SNRdB)+3).^4.8);
%% G: Generator Matrix, H: Paritycheck Matrix
G=bem_hammgen(Kc);
% Change Generator Matrix to extended Hamming Code
if ExtHammCode==1
G=extHammG(G);
end
kc=size(G,1); % Number of information bits
nc=size(G,2); Kc=nc-kc; % Code word length
Rc=(kc)/(nc); % Code rate Rc
EbN0=SNRdB-10*log10(Rc); % Eb/N0
H = gen2par(G); % generate H from G
HT=H.'; % Transpose
%% Permutation of 1,2 and 3 bit errors
[e1, e2, e3]=permute_e(nc,M);
e=[e1;e2;e3];
%% syndrom calculation
syn=NaN(size(e,1),Kc);
for k=1:size(e,1)
syn(k,:)=mod(e(k,:)*HT,2);
end
%% sort rows of syndroms associated error pattern e
[s_sort,s_idx] = sortrows(syn); % sort syn to s_sort
e_sort=e(s_idx,:); % sort e to e_sort in the same way as syn
e_sort=e_sort(sum(s_sort,2)>0,:); % delete zero rows
s_sort=s_sort(sum(s_sort,2)>0,:); % delete zero rows
% s_de=bi2de(s_sort,[],'left-msb'); % Communication Toolbox function
s_de=bem_bi2de(s_sort); % calculate decimal values from s_sort
s_pdf=hist(s_de,1:2^Kc-1); % calculate which value occurs how often
%s_pdf(s_pdf==0)=[];
%% Loops for BER calculation
tic
sigma = sqrt(10.^(-SNRdB./10)); % standard diviation of noise
BER_dec_mean=zeros(1,length(SNRdB)); % mean of BER for coded system
BER_mean=zeros(1,length(SNRdB)); % mean of BER for uncoded system
for zzz=1:length(SNRdB)
%disp(num2str(zzz))
for kkk=1:K_loop(zzz)
%% random bits
x_msg=round(rand(Nframes,kc));
%% channel coding
x_code=mod(x_msg*G,2);
%% Modulation and Noise
x_mod = -(x_code-0.5)*2+1i*1E-99;
noi=1/sqrt(2)*(randn(Nframes,nc)+1i*randn(Nframes,nc))*sigma(zzz);
x_r=x_mod+noi;
%% Demodulation
x_llr = real(x_r)*4/sigma(zzz).^2; % Calculate Log-Likelihood Ratios
x_code_r=(sign(-x_llr)+1)/2; % Received bit stream
%% BER uncoded
bit_err=abs(x_code-x_code_r);
BER=sum(bit_err(:))/(Nframes*nc);
BER_mean(zzz)=BER_mean(zzz)+BER;
%% Decoding
[x_decode,x_llr_new] = hamm_soft_out(HT,e_sort,s_pdf,x_llr);
%[x_decode] = hamm_soft_really_fast(HT,e_sort,s_sort,x_llr,Kc);
%% BER coded
dec_err=abs(x_code-x_decode);
BER_dec=sum(dec_err(:))/(Nframes*nc);
BER_dec_mean(zzz)=BER_dec_mean(zzz)+BER_dec;
end
BER_mean(zzz)=BER_mean(zzz)/K_loop(zzz);
BER_dec_mean(zzz)=BER_dec_mean(zzz)/K_loop(zzz);
disp(['Eb/N0=' num2str(EbN0(zzz)) ...
'; BER_uncoded=' num2str(BER_mean(zzz)) ...
'; BER_coded=' num2str(BER_dec_mean(zzz))]);
end
toc
DN='displayname';
Co='Color';
Ma='Marker';
if length(SNRdB)>1
figure(1);hold off
semilogy(SNRdB,BER_mean,Co,[0 0 0],Ma,'o',DN,'uncoded');
hold on; grid on;
semilogy(EbN0,BER_dec_mean,Co,[0 0 0],Ma,'.',...
DN,[num2str(nc) ',' num2str(kc) '-Hamming code, ' 'M=' num2str(M)]);
xlabel('E_b/N_0 in dB')
ylabel('BER')
legend show
end
A_101
