cyclgen.m

数字通信第四版原书的例程

function [h, g, k] = cyclgen(n, p, opt)
%CYCLGEN Produces cyclic code generator matrix in GF(2).
%       H = CYCLGEN(N, P) produces the parity-check matrix for a given
%       codeword length N and generates polynomial P. Polynomial P can
%       generate a cyclic code only if P is a factor of polynomial X^N-1.
%       The message length of the coding is K = N - M where M is the degree
%       of P. The parity-check matrix is an M-by-N matrix.
%
%       H = CYCLGEN(N, P, OPT) produces the parity-check matrix based on the
%       instruction given in OPT. When
%       OPT = 'nonsys', the function produces a non-systematic cyclic parity-
%                       check matrix;
%       OPT = 'system', the function produces a systematic cyclic parity-check
%                       matrix. This option is the default.
%
%       [H, G] = CYCLGEN(...) produces the generator matrix G as well as the 
%       generator matrix G. The parity-check matrix is an K-by-N matrix,
%       where K = N - M;
%
%       [H, G, K] = CYCLGEN(...) outputs the message length K.
%
%       See also ENCODE, DECODE, BCHPOLY, CYCLPOLY.

%       Wes Wang 6/23/94
%       Copyright (c) 1995-96 by The MathWorks, Inc.
%       $Revision: 1.1 $  $Date: 1996/04/01 17:55:55 $

if nargin < 2
    error('Not enough input parameters')
elseif nargin < 3
    opt = 'system';
else
    opt = lower(opt);
end;

p = p(:)';
m = length(p) - 1;
k = n - m;

% verify if the polynomial is a irreducible
[pc, r] = gfdeconv([1 zeros(1, n-1) 1], p);
if max(r) ~= 0
    error('Generator polynomial P cannot produce cyclic code generator matrix');
end;

if ~isempty(findstr(opt, 'no'))
    % generate the regular cyclic code matrices
    
    % parity-check matrix
    tmp = [fliplr(pc), zeros(1, n-k-1)];
    h = [];
    for i = 1 : n-k
        h = [h; tmp];
        tmp = [tmp(n), tmp(1:n-1)];
    end;

    % generator matrix
    if nargin > 1
        tmp = [p(:)', zeros(1,n-m-1)];
        g = [];
        for i=1:k
            g = [g; tmp];
            tmp = [tmp(n), tmp(1:n-1)];
        end;
    end;

else
    % generate systematic cyclic code matrices
    
    % parity check matrix
    b = [];
    for i = 0 : k-1
        [q, tmp] = gfdeconv([zeros(1, n-k+i), 1], p);
        tmp = [tmp zeros(1, m-length(tmp))];
        b = [b; tmp];
    end;
    h = [eye(n-k), b'];

    % generator matrix
    g = [b eye(k)];

end

%--end of cyclgen--