rspoly.m

经典通信系统仿真书籍《通信系统与 MATLAB (Proakis)》源代码

function [pg, t] = rspoly(n, k, tp)
%RSPOLY Produces Reed-Solomon code generator polynomial.
%       Pg = RSPOLY(N, K) outputs the generator polynomial of Reed-Solomon
%       code with codeword length N, message length K. A valid N should be
%       2^M-1, where M is an integer no less than 3. K should be an odd
%       positive number. The error-correction capability is (N - K) / 2. The
%       output Pg is a polynomial in GF(2^M). Each element is represented by
%       the power form.
%
%       Pg = RSPOLY(N, K, TP) produces generator polynomials using the
%       specified GF(2^M) element list. TP is a (N+1)-by-M matrix, where
%       N = 2^M-1. When TP is a scalar, it specifies M. This form is suggested
%       to speed up the calculation.
%
%       [Pg, T] = RSPOLY(N, K) outputs the error-correction capability of the
%       RS code.
%
%       See also ENCODE, DECODE.

%       Wes Wang 8/8/94, 10/11/95.
%       Copyright (c) 1995-96 by The MathWorks, Inc.
%       $Revision: 1.1 $  $Date: 1996/04/01 18:03:15 $

if nargin < 2
    error('Not enough input variable')
end;

if nargin < 3
    % find the m from n
    dim = 3;
    pow_dim = 2^dim -1;
    while pow_dim < n
        dim = dim + 1;
        pow_dim = 2^dim - 1;
    end;
    tp = gftuple([-1:n-1]',dim);
else
    if length(tp) == 1
        dim = tp;
        tp = gftuple([-1:n-1]',dim);
    end
    [n_tp, dim] = size(tp);
    if n_tp ~= n+1
        error('The input parameters N and TP conflict');
    end;
    pow_dim = 2^dim - 1;
end;

if n ~= pow_dim
    error('The code word length N must be 2^M -1, where M is an integer');
end;

if (floor(n) ~= n) | (floor(k) ~= k)
    error('The input dimension parameters must be integer')
end;

t2 = n - k;

%%% find the generator polynomial by multiply
% g(X) = (X + alpha)(X + alpha^2)(X + alpha^3)...(X + alpha^(2t-1))(X + alpha^(2t))
%      = g_0 + g_1 X + g_2 X^2 + ... + g_(2t - 1) X^(2t - 1) + X^2t
%
% using the algorithm used in poly
pg = [0, -ones(1, t2)];
alpha = [1 : t2];
for i = 1 : t2
    pg(2:(i+1)) = gfadd(pg(2:(i+1)), gfmul(pg(1:i), alpha(i), tp), tp);
end;
pg = fliplr(pg);
% finished pg built up

% error-correction capability
t = floor(t2/2);
% finished error-correction fingure.