递归系统卷积码译码_递归系统卷积码的状态转移 | 学步园

令 生成多项式为：G(7，5)=[1 1 1；1 0 1]    注意是系统码

第一种方法：

a= poly2trellis(3, [7 5],7);

>> a.nextStates

ans =

0 2

2 0

3 1

1 3

第二种方法：

function [next_out, next_state, last_out, last_state] = trellis(g)

% copyright Nov. 1998 Yufei Wu

% MPRG lab, Virginia Tech

% for academic use only

% set up the trellis given code generator g

% g given in binary matrix form. e.g. g = [ 1 1 1; 1 0 1 ];

% next_out(i,1:2): trellis next_out (systematic bit; parity bit) when input = 0, state = i; next_out(i,j) = -1 or 1

% next_out(i,3:4): trellis next_out (systematic bit; parity bit) when input = 1, state = i;

% next_state(i,1): next state when input = 0, state = i; next_state(i,i) = 1,...2^m

% next_state(i,2): next state when input = 1, state = i;

% last_out(i,1:2): trellis last_out (systematic bit; parity bit) when input = 0, state = i; last_out(i,j) = -1 or 1

% last_out(i,3:4): trellis last_out (systematic bit; parity bit) when input = 1, state = i;

% last_state(i,1): previous state that comes to state i when info. bit = 0;

% last_state(i,2): previous state that comes to state i when info. bit = 1;

[n,K] = size(g);

m = K - 1;

max_state = 2^m;

% set up next_out and next_state matrices for systematic code

for state=1:max_state

state_vector = bin_state( state-1, m );

% when receive a 0

d_k = 0;

a_k = rem( g(1,:)*[0 state_vector]', 2 );

[out_0, state_0] = encode_bit(g, a_k, state_vector);

out_0(1) = 0;

% when receive a 1

d_k = 1;

a_k = rem( g(1,:)*[1 state_vector]', 2 );

[out_1, state_1] = encode_bit(g, a_k, state_vector);

out_1(1) = 1;

next_out(state,:) = 2*[out_0 out_1]-1;

next_state(state,:) = [(int_state(state_0)+1) (int_state(state_1)+1)];

end

% find out which two previous states can come to present state

last_state = zeros(max_state,2);

for bit=0:1

for state=1:max_state

last_state(next_state(state,bit+1), bit+1)=state;

last_out(next_state(state, bit+1), bit*2+1:bit*2+2) ...

= next_out(state, bit*2+1:bit*2+2);

end

end

g = [ 1 1 1; 1 0 1 ];

>> [next_out, next_state, last_out, last_state] = trellis(g)

next_out =

-1 -1 1 1

-1 -1 1 1

-1 1 1 -1

-1 1 1 -1

next_state =

1 3

3 1

4 2

2 4

last_out =

-1 -1 1 1

-1 1 1 -1

-1 -1 1 1

-1 1 1 -1

last_state =

1 2

4 3

2 1

3 4

第三种方法：

function [ lstate ,nstate ,lparoutput ] = gen_trellis(g)

%generate trellis

%Output:

% lstate --2 by x matrix, lstate(linput,cstate)=laststate

% --where linput=1(correspond to 0), 2(correspond to 1)

% nstate --2 by x matrix, nstate(cinput,cstate)=nextstate

% lparoutput --2 by x matrix, lparoutput(cinput,cstate)=lastparityoutput 前向的输出

% --where cinput=1(correspond to 0), 2(correspond to 1)

%

% chenxiao, 2010.7, SEU, Email:chenxiao20072008@gmail.com

[~,K] = size(g);

m = K - 1; % determine the memory

nstate=zeros(2,2^m); % preallocate for speed

lstate=zeros(2,2^m); % preallocate for speed

lparoutput=zeros(2,2^m); % preallocate for speed

for i=1:2^m

state_temp=de2bi(i-1,m); % decimal to binary, see help for details

%input 0

state=fliplr(state_temp); % state, corresponding to decimal value 1,2,...,2^m

in=xor(rem(g(1,2:end)*state',2),0); % input 0

paroutput=rem(g(2,:)*[in state]',2);

state=[in,state(1:m-1)];

nstate_index=bi2de(fliplr(state))+1; % see help for details

nstate(1,i)=nstate_index; % next state

lparoutput(1,nstate_index)=2*paroutput-1; % last parity output

lstate(1,nstate_index)=i; % last state

%input 1

state=fliplr(state_temp);

in=xor(rem(g(1,2:end)*state',2),1); % input 1

paroutput=rem(g(2,:)*[in state]',2);

state=[in,state(1:m-1)];

nstate_index=bi2de(fliplr(state))+1; % see help for details

nstate(2,i)=nstate_index; % next state

lparoutput(2,nstate_index)=2*paroutput-1; % last parity output

lstate(2,nstate_index)=i; % last state

end

>> g = [ 1 1 1; 1 0 1 ];

>> [ lstate ,nstate ,lparoutput ] = gen_trellis(g)

lstate =

1 4 2 3

2 3 1 4

nstate =

1 3 4 2

3 1 2 4

lparoutput =

-1 1 -1 1

1 -1 1 -1

补充：

如果 G(13 ,15) = [1 0 1  1 ;  1 1 0 1  ]

poly2trellis(4, [13 15 ], 13)

function [ lstate ,nstate ,lparoutput,nparaout] = gen_trellis(g)

%generate trellis

%Output:

% lstate --2 by x matrix, lstate(linput,cstate)=laststate

% --where linput=1(correspond to 0), 2(correspond to 1)

% nstate --2 by x matrix, nstate(cinput,cstate)=nextstate

% lparoutput --2 by x matrix, lparoutput(cinput,cstate)=lastparityoutput 前向的输出

% --where cinput=1(correspond to 0), 2(correspond to 1)

%

% chenxiao, 2010.7, SEU, Email:chenxiao20072008@gmail.com

%g=[1 0 1 1 ;1 1 0 1];

[~,K] = size(g);

m = K - 1; % determine the memory

nstate=zeros(2,2^m); % preallocate for speed

lstate=zeros(2,2^m); % preallocate for speed

lparoutput=zeros(2,2^m); % preallocate for speed

for i=1:2^m

state_temp=de2bi(i-1,m); % decimal to binary, see help for details

%input 0

state=fliplr(state_temp); % state, corresponding to decimal value 1,2,...,2^m

in=xor(rem(g(1,2:end)*state',2),0); % input 0

paroutput=rem(g(2,:)*[in state]',2);

state=[in,state(1:m-1)];

nstate_index=bi2de(fliplr(state))+1; % see help for details

nstate(1,i)=nstate_index; % next state

lparoutput(1,nstate_index)=2*paroutput-1; % last parity output

lstate(1,nstate_index)=i; % last state

%input 1

state=fliplr(state_temp);

in=xor(rem(g(1,2:end)*state',2),1); % input 1

paroutput=rem(g(2,:)*[in state]',2);

state=[in,state(1:m-1)];

nstate_index=bi2de(fliplr(state))+1; % see help for details

nstate(2,i)=nstate_index; % next state

lparoutput(2,nstate_index)=2*paroutput-1; % last parity output

lstate(2,nstate_index)=i; % last state

end

%以下为计算next paraout

[m,n] =size (lparoutput) ;

temp = zeros(n,2*m) ;

temp (:,1 : 2*m) =[ lstate(1,:) .' lparoutput(1,:).' lstate(2,:) .' lparoutput(2,:).' ] ;

nparaout = zeros(m,n) ;

temp(:,1:2 ) = sortrows(temp(:,1:2),1) ;

temp(:,3:4 ) = sortrows(temp(:,3:4),1) ;

nparaout = [temp(:,2).' ; temp(:,4).' ] ;