Communications Toolbox

bchdeco

BCH decoder

Syntax

• msg = bchdeco(code,k,t);
  msg = bchdeco(code,k,t,prim_poly); 
  [msg,err] = bchdeco(...);
  [msg,err,ccode] = bchdeco(...);
  

Description

msg = bchdeco(code,k,t) decodes code using the BCH method. k is the message length. The codeword length n must have the form 2^m-1 for some integer m greater than or equal to 3. code is a binary matrix with n columns, each row of which represents one codeword. msg is a binary matrix with k columns, each row of which represents one message. t is the error-correction capability. BCH decoding requires a primitive polynomial for GF(2^m); this syntax uses the default primitive polynomial, gfprimdf(m).

msg = bchdeco(code,k,t,prim_poly) is the same as the first syntax, except that prim_poly is a row vector that gives the coefficients, in order of ascending powers, of the primitive polynomial for GF(2^m) that will be used during processing.

[msg,err] = bchdeco(...) returns a column vector err that gives information about error correction. A nonnegative integer in err(r) indicates the number of errors corrected in the rth codeword; a negative integer indicates that there are more errors in the rth codeword than can be corrected.

[msg,err,ccode] = bchdeco(...) returns the corrected code in ccode.

Examples

The script below encodes a (random) message, simulates the addition of noise to the code, and then decodes the message.

• m = 4; n = 2^m-1; % Codeword length
  params = bchpoly(n); 
  % Arbitrarily focus on 3rd row of params.
  k = params(3,2); % Codeword length
  t = params(3,3); % Error-correction capability
  msg = randint(100,k);
  code = bchenco(msg,n,k); % Encode the message.
  % Corrupt up to t bits in each codeword.
  noisycode = rem(code + randerr(100,n,1:t),2);
  % Decode the noisy code.
  [newmsg,err,ccode] = bchdeco(noisycode,k,t); 
  if ccode==code
     disp('All errors were corrected.')
  end
  if newmsg==msg
     disp('The message was recovered perfectly.')
  end
  

In this case, all errors are corrected and the message is recovered perfectly. However, if the ninth line is changed to

• noisycode = rem(code + randerr(100,n,1:(t+1)),2);
  

then some codewords will contain more than t errors. This is too many errors, and some will go uncorrected.

See Also
bchenco, bchpoly

awgn

bchenco