trellis.m

This matlab code on reed solomon and BCH encoding and different decoding algorithms. Also errors and

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