function [decoder_output,survivor_state,cumulated_metric]=viterbi(G,k,channel_output)
% [decoder_output,survivor_state,cumulated_metric]=viterbi(G,k,channel_output)
% 其中G是一個(gè)n行L*k列矩陣，它的每一行決定了從移位寄存器到輸入碼字的連接方式.
% survivor_state是一個(gè)矩陣，它顯示了通過網(wǎng)格的最優(yōu)路徑，這個(gè)矩陣通過一個(gè)單獨(dú)
% 的函數(shù)metric(x,y)給出，這個(gè)算法既能用于硬判決譯碼也能用于軟判決譯碼。


% k=1;
% G=[1 1 1;1 0 1];
n=size(G,1);
%檢驗(yàn)G的維數(shù) 
if rem(size(G,2),k)~=0
    error('Size of G and k do not agree')
end
if rem(size(channel_output,2),n)~=0
    error('channle output not of the right size')
end
L=size(G,2)/k;
number_of_states=2^((L-1)*k);

%產(chǎn)生狀態(tài)轉(zhuǎn)移矩陣，輸出矩陣和輸入矩陣 
for j=0:number_of_states-1
    for t=0:2^k-1
        [next_state,memory_contents]=nxt_stat(j,t,L,k);
        input(j+1,next_state+1)=t;
        branch_output=rem(memory_contents*G',2);
        nextstate(j+1,t+1)=next_state;
        output(j+1,t+1)=bin2deci(branch_output);
    end
end
input;
state_metric=zeros(number_of_states,2);
depth_of_trellis=length(channel_output)/n;
channel_output_matrix=reshape(channel_output,n,depth_of_trellis);
survivor_state=zeros(number_of_states,depth_of_trellis+1);
[row_survivor col_survivor]=size(survivor_state);
%開始非尾信道輸出的解碼 
%i為段，j為每一階段的狀態(tài)，t為輸入
for i=1:depth_of_trellis-L+1
    flag=zeros(1,number_of_states);

    if i<=L
        step=2^((L-i)*k);
    else
        step=1;
    end
    for j=0:step:number_of_states-1
        for t=0:2^k-1
            branch_metric=0;
            binary_output=deci2bin(output(j+1,t+1),n);
            for tt=1:n
                branch_metric=branch_metric+metric(channel_output_matrix(tt,i),binary_output(tt));
            end
            if ((state_metric(nextstate(j+1,t+1)+1,2)>state_metric(j+1,1)+branch_metric)|flag(nextstate(j+1,t+1)+1)==0)
                state_metric(nextstate(j+1,t+1)+1,2)=state_metric(j+1,1)+branch_metric;
                survivor_state(nextstate(j+1,t+1)+1,i+1)=j;
                flag(nextstate(j+1,t+1)+1)=1;
            end
        end
    end
    state_metric=state_metric(:,2:-1:1);
end


%開始尾信道輸出的解碼 
for i=depth_of_trellis-L+2:depth_of_trellis
    flag=zeros(1,number_of_states);
    last_stop=number_of_states/(2^((i-depth_of_trellis+L-2)*k));
    for j=0:last_stop-1
        branch_metric=0;
        binary_output=deci2bin(output(j+1,1),n);
        for tt=1:n
            branch_metric=branch_metric+metric(channel_output_matrix(tt,i),binary_output(tt));
        end
        if ((state_metric(nextstate(j+1,1)+1,2)>state_metric(j+1,1)+branch_metric)|flag(nextstate(j+1,1)+1)==0)
            state_metric(nextstate(j+1,1)+1,2)=state_metric(j+1,1)+branch_metric;
            survivor_state(nextstate(j+1,1)+1,i+1)=j;
            flag(nextstate(j+1,1)+1)=1;
        end
    end
    state_metric=state_metric(:,2:-1:1);
end

%從最優(yōu)路徑產(chǎn)生解碼輸出 
%由段得到狀態(tài)序列，再由狀序列從input矩陣中得到該段的輸出
state_sequence=zeros(1,depth_of_trellis+1);
size(state_sequence);
state_sequence(1,depth_of_trellis)=survivor_state(1,depth_of_trellis+1);
for i=1:depth_of_trellis
   state_sequence(1,depth_of_trellis-i+1)=survivor_state((state_sequence(1,depth_of_trellis+2-i)+1),depth_of_trellis-i+2);
end
state_sequence;
decoder_output_matrix=zeros(k,depth_of_trellis-L+1);
for i=1:depth_of_trellis-L+1
    dec_output_deci=input(state_sequence(1,i)+1,state_sequence(1,i+1)+1);
    dec_output_bin=deci2bin(dec_output_deci,k);
    decoder_output_matrix(:,i)=dec_output_bin(k:-1:1)';
end
decoder_output=reshape(decoder_output_matrix,1,k*(depth_of_trellis-L+1));
cumulated_metric=state_metric(1,1);