遞迴系統卷積碼的狀態轉移
阿新 • • 發佈：2019-01-02
令 生成多項式為：G（7，5）=[1 1 1；1 0 1] 注意是系統碼
第一種方法：
a= poly2trellis(3, [7 5],7);
>> a.nextStates
ans =
0 2
2 0
3 1
1 3function [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
第三種方法：
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 前向的輸出
% --where cinput=1(correspond to 0), 2(correspond to 1)
%
% chenxiao, 2010.7, SEU, Email: >> 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補充：
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 前向的輸出
% --where cinput=1(correspond to 0), 2(correspond to 1)
%
% chenxiao, 2010.7, SEU, Email:[email protected]
%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
%以下為計算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).' ] ;