function [msg, err, ccode] = rsdecode(code, k, tp)
%RSDECODE Reed-Solomon decode.
%       MSG = RSDECODE(CODE, K) recovers the message information from code
%       word CODE, which has been coded using Reed-Solomon encoding technique.
%       CODE is a matrix with the row length being N = 2^M - 1, where
%       M is a positive integer no less than 3. K is the message length.
%       Usually, the message length is an odd number. The error-correction
%       capability of a Reed-Solomon code is T = floor((M - K) / 2). The
%       recovered message store in MSG. The row number of MSG is the same as
%       the row number of CODE. The column number of MSG is K. Note the 
%       difference from all of the other encoding/decoding functions.
%       This function takes the exponential input instead of regular input
%       for processing. For example [-Inf, 0, 1, 2, ...] represents
%       [0 1 alpha, alpha^2, ...] in GF(2^m). There are 2^M elements in
%       GF(2^M). Hence, the input CODE represents 2^M * (2^M - 1) bits of
%       information. The decoded MSG represents 2^M * K bits of information.
%
%       MSG = RSDECODE(CODE, K, TP) recovers the length K message information
%       from code word CODE with specified GF(2^M) elements in TP. This
%       format is recommended even if the GF(2^M) is a default one in speeding
%       up the process. A default TP can be generated by using
%       TP = gftuple([-1:2^M-2]',M);
%
%       [MSG, ERR] = RSDECODE(...) provides the error correction information. 
%       A non-negative positive element in ERR indicates the number of errors
%       has been corrected. A negative element in ERR indicates there are more
%       errors encountered in the decode than it can correct.
%
%       [MSG, ERR, CCODE] = RSDECODE(...) provides the corrected code word in
%       CCODE.
%
%       Example of using the function:
%       M = 4;                      % M is a number larger or equal to 3.
%       N = 2^M - 1;                % The code word length.
%       K = 9;                      % K is the message length.
%       T = floor((N - K)/2);       % Error-correction capability.
%       NUM_ROW = 10;               % Number of rows in the calculation
%       MSG = randint(NUM_ROW, K, [-1, N-1])
%                                   % Generate a random number. Note that
%                                   % a "-1" is equivalent to "-Inf".
%       TP = gftuple([-1:N-1]', M); % A complete list of all elements in
%                                   % GF(2^M).
%       PG = rspoly(N, K);          % Produce generator polynomial.
%       CODE =rsencode(MSG,PG,N,TP);% Reed-Solomon encode calculation.
%       CODE_NOI = CODE + randbit(NUM_ROW, N, [1 1 1]/4);
%       DEC = rsdecode(CODE_NOI, K, TP) % Reed-Solomon decode calculation.
%       
%       See also RSENCODE, RSCORE.

%       Wes Wang 8/10/94
%       Copyright (c) 1995-96 by The MathWorks, Inc.
%       $Revision: 1.1 $  $Date: 1996/04/01 18:02:47 $

% build tp if it is not given
if nargin < 2
    error('Not enough input parameters.')
end;

%fprintf('Reed-Solomon decode calculation. Please wait..\n.');
[n_code, m_code] = size(code);
t2 = m_code - k;

if nargin < 3
    % find dim from m_code
    dim = 3;
    pow_dim = 2^dim -1;
    while pow_dim < m_code
        dim = dim + 1;
        pow_dim = 2^dim - 1;
    end;
    tp = gftuple([-1:pow_dim-1]', dim);
else
    if length(tp) == 1
        dim = tp;
        pow_dim = 2^dim - 1;
        tp = gftuple([-1:pow_dim-1]', dim);
    else
        [pow_dim, dim] = size(tp);
        pow_dim = pow_dim - 1;
    end;
end;

if m_code ~= pow_dim
    error('The length of the code word is not a valid one');
end;

for i = 1 : n_code
%    if rem(i, 40)
%        fprintf('.');
%    else
%        fprintf([num2str(i/n_code*100),'%%\n.']);
%    end;
    [msg(i, :), err(i), ccode(i, :)] = rscore(code(i,:), k, tp, dim, pow_dim);
end;
err = err(:);
%fprintf('. done.\n');
% -- end of rsdecode.m --