--- /dev/null
+## Copyright (C) 2003 David Bateman
+##
+## This program is free software; you can redistribute it and/or modify it under
+## the terms of the GNU General Public License as published by the Free Software
+## Foundation; either version 3 of the License, or (at your option) any later
+## version.
+##
+## This program is distributed in the hope that it will be useful, but WITHOUT
+## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more
+## details.
+##
+## You should have received a copy of the GNU General Public License along with
+## this program; if not, see <http://www.gnu.org/licenses/>.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {@var{msg} =} decode (@var{code},@var{n},@var{k})
+## @deftypefnx {Function File} {@var{msg} =} decode (@var{code},@var{n},@var{k},@var{typ})
+## @deftypefnx {Function File} {@var{msg} =} decode (@var{code},@var{n},@var{k},@var{typ},@var{opt1})
+## @deftypefnx {Function File} {@var{msg} =} decode (@var{code},@var{n},@var{k},@var{typ},@var{opt1},@var{opt2})
+## @deftypefnx {Function File} {[@var{msg}, @var{err}] =} decode (@var{...})
+## @deftypefnx {Function File} {[@var{msg}, @var{err}, @var{ccode}] =} decode (@var{...})
+## @deftypefnx {Function File} {[@var{msg}, @var{err}, @var{ccode}, @var{cerr}] =} decode (@var{...})
+##
+## Top level block decoder. This function makes use of the lower level
+## functions such as @dfn{cyclpoly}, @dfn{cyclgen}, @dfn{hammgen}, and
+## @dfn{bchenco}. The coded message to decode is pass in @var{code}, the
+## codeword length is @var{n} and the message length is @var{k}. This
+## function is used to decode messages using either:
+##
+## @table @asis
+## @item A [n,k] linear block code defined by a generator matrix
+## @item A [n,k] cyclic code defined by a generator polynomial
+## @item A [n,k] Hamming code defined by a primitive polynomial
+## @item A [n,k] BCH code code defined by a generator polynomial
+## @end table
+##
+## The type of coding to use is defined by the variable @var{typ}. This
+## variable is a string taking one of the values
+##
+## @table @code
+## @item 'linear' or 'linear/binary'
+## A linear block code is assumed with the message @var{msg} being in a
+## binary format. In this case the argument @var{opt1} is the generator
+## matrix, and is required. Additionally, @var{opt2} containing the
+## syndrome lookup table (see @dfn{syndtable}) can also be passed.
+## @item 'cyclic' or 'cyclic/binary'
+## A cyclic code is assumed with the message @var{msg} being in a binary
+## format. The generator polynomial to use can be defined in @var{opt1}.
+## The default generator polynomial to use will be
+## @dfn{cyclpoly(@var{n},@var{k})}. Additionally, @var{opt2} containing the
+## syndrome lookup table (see @dfn{syndtable}) can also be passed.
+## @item 'hamming' or 'hamming/binary'
+## A Hamming code is assumed with the message @var{msg} being in a binary
+## format. In this case @var{n} must be of an integer of the form
+## @code{2^@var{m}-1}, where @var{m} is an integer. In addition @var{k}
+## must be @code{@var{n}-@var{m}}. The primitive polynomial to use can
+## be defined in @var{opt1}. The default primitive polynomial to use is
+## the same as defined by @dfn{hammgen}. The variable @var{opt2} should
+## not be defined.
+## @item 'bch' or 'bch/binary'
+## A BCH code is assumed with the message @var{msg} being in a binary
+## format. The primitive polynomial to use can be defined in @var{opt2}.
+## The error correction capability of the code can also be defined in
+## @var{opt1}. Use the empty matrix [] to let the error correction
+## capability take the default value.
+## @end table
+##
+## In addition the argument 'binary' above can be replaced with 'decimal',
+## in which case the message is assumed to be a decimal vector, with each
+## value representing a symbol to be coded. The binary format can be in two
+## forms
+##
+## @table @code
+## @item An @var{x}-by-@var{n} matrix
+## Each row of this matrix represents a symbol to be decoded
+## @item A vector with length divisible by @var{n}
+## The coded symbols are created from groups of @var{n} elements of this vector
+## @end table
+##
+## The decoded message is return in @var{msg}. The number of errors encountered
+## is returned in @var{err}. If the coded message format is 'decimal' or a
+## 'binary' matrix, then @var{err} is a column vector having a length equal
+## to the number of decoded symbols. If @var{code} is a 'binary' vector, then
+## @var{err} is the same length as @var{msg} and indicated the number of
+## errors in each symbol. If the value @var{err} is positive it indicates the
+## number of errors corrected in the corresponding symbol. A negative value
+## indicates an uncorrectable error. The corrected code is returned in
+## @var{ccode} in a similar format to the coded message @var{msg}. The
+## variable @var{cerr} contains similar data to @var{err} for @var{ccode}.
+##
+## It should be noted that all internal calculations are performed in the
+## binary format. Therefore for large values of @var{n}, it is preferable
+## to use the binary format to pass the messages to avoid possible rounding
+## errors. Additionally, if repeated calls to @dfn{decode} will be performed,
+## it is often faster to create a generator matrix externally with the
+## functions @dfn{hammgen} or @dfn{cyclgen}, rather than let @dfn{decode}
+## recalculate this matrix at each iteration. In this case @var{typ} should
+## be 'linear'. The exception to this case is BCH codes, where the required
+## syndrome table is too large. The BCH decoder, decodes directly from the
+## polynomial never explicitly forming the syndrome table.
+##
+## @end deftypefn
+## @seealso{encode,cyclgen,cyclpoly,hammgen,bchdeco,bchpoly,syndtable}
+
+function [msg, err, ccode, cerr] = decode(code, n, k, typ, opt1, opt2)
+
+ if ((nargin < 3) || (nargin > 6))
+ usage ("[msg, err, ccode] = decode (code, n, k [, typ [, opt1 [, opt2]]])");
+ endif
+
+ if (!isscalar(n) || (n != floor(n)) || (n < 3))
+ error ("decode: codeword length must be an integer greater than 3");
+ endif
+
+ if (!isscalar(k) || (k != floor(k)) || (k > n))
+ error ("decode: message length must be an integer less than codeword length");
+ endif
+
+ if (nargin > 3)
+ if (!ischar(typ))
+ error ("decode: type argument must be a string");
+ else
+ ## Why the hell did matlab decide on such an ugly way of passing 2 args!
+ if (strcmp(typ,"linear") || strcmp(typ,"linear/binary"))
+ coding = "linear";
+ msgtyp = "binary";
+ elseif (strcmp(typ,"linear/decimal"))
+ coding = "linear";
+ msgtyp = "decimal";
+ elseif (strcmp(typ,"cyclic") || strcmp(typ,"cyclic/binary"))
+ coding = "cyclic";
+ msgtyp = "binary";
+ elseif (strcmp(typ,"cyclic/decimal"))
+ coding = "cyclic";
+ msgtyp = "decimal";
+ elseif (strcmp(typ,"bch") || strcmp(typ,"bch/binary"))
+ coding = "bch";
+ msgtyp = "binary";
+ elseif (strcmp(typ,"bch/decimal"))
+ coding = "bch";
+ msgtyp = "decimal";
+ elseif (strcmp(typ,"hamming") || strcmp(typ,"hamming/binary"))
+ coding = "hamming";
+ msgtyp = "binary";
+ elseif (strcmp(typ,"hamming/decimal"))
+ coding = "hamming";
+ msgtyp = "decimal";
+ else
+ error ("decode: unrecognized coding and/or message type");
+ endif
+ endif
+ else
+ coding = "hamming";
+ msgtyp = "binary";
+ endif
+
+ if (strcmp(msgtyp,"binary"))
+ vecttyp = 0;
+ if ((max(code(:)) > 1) || (min(code(:)) < 0))
+ error ("decode: illegal value in message");
+ endif
+ [ncodewords, n2] = size(code);
+ len = n2*ncodewords;
+ if ((n * floor(len/n)) != len)
+ error ("decode: coded message of incorrect length");
+ endif
+ if (min(n2,ncodewords) == 1)
+ vecttyp = 1;
+ ncodewords = len / n;
+ code = reshape(code,n,ncodewords);
+ code = code';
+ elseif (n2 != n)
+ error ("decode: coded message matrix must be n columns wide");
+ endif
+ else
+ if (!isvector(code))
+ error ("decode: decimally decoded message must be a vector");
+ endif
+ if ((max(code) > 2^n-1) || (min(code) < 0))
+ error ("decode: illegal value in message");
+ endif
+ ncodewords = length(code);
+ code = de2bi(code(:),n);
+ endif
+
+ if (strcmp(coding,"bch"))
+ if ((nargin < 5) || (isempty(opt1)))
+ tmp = bchpoly(n, k,"probe");
+ t = tmp(3);
+ else
+ t = opt1;
+ endif
+
+ if (nargin > 5)
+ [msg err ccode] = bchdeco(code,k,t,opt2);
+ else
+ [msg err ccode] = bchdeco(code,k,t);
+ endif
+ cerr = err;
+ else
+ if (strcmp(coding,"linear"))
+ if (nargin > 4)
+ gen = opt1;
+ if ((size(gen,1) != k) || (size(gen,2) != n))
+ error ("decode: generator matrix is in incorrect form");
+ endif
+ par = gen2par(gen);
+ if (nargin > 5)
+ st = opt2;
+ else
+ st = syndtable(par);
+ endif
+ else
+ error ("decode: linear coding must supply the generator matrix");
+ endif
+ elseif (strcmp(coding,"cyclic"))
+ if (nargin > 4)
+ [par, gen] = cyclgen(n,opt1);
+ else
+ [par, gen] = cyclgen(n,cyclpoly(n,k));
+ endif
+ if (nargin > 5)
+ ## XXX FIXME XXX Should we check that the generator polynomial is
+ ## consistent with the syndrome table. Where is the acceleration in
+ ## this case???
+ st = opt2;
+ else
+ st = syndtable(par);
+ endif
+ else
+ m = log2(n + 1);
+ if ((m != floor(m)) || (m < 3) || (m > 16))
+ error ("decode: codeword length must be of the form '2^m-1' with integer m");
+ endif
+ if (k != (n-m))
+ error ("decode: illegal message length for hamming code");
+ endif
+ if (nargin > 4)
+ [par, gen] = hammgen(m, opt1);
+ else
+ [par, gen] = hammgen(m);
+ endif
+ if (nargin > 5)
+ error ("decode: illegal call for hamming coding");
+ else
+ st = syndtable(par);
+ endif
+ endif
+
+ errvec = st(bi2de((mod(par * code',2))',"left-msb")+1,:);
+ ccode = mod(code+errvec,2);
+ err = sum(errvec');
+ cerr = err;
+ if (isequal(gen(:,1:k),eye(k)))
+ msg = ccode(:,1:k);
+ elseif (isequal(gen(:,n-k+1:n),eye(k)))
+ msg = ccode(:,n-k+1:n);
+ else
+ error ("decode: generator matrix must be in standard form");
+ endif
+ endif
+
+ if (strcmp(msgtyp,"binary") && (vecttyp == 1))
+ msg = msg';
+ msg = msg(:);
+ ccode = ccode';
+ ccode = ccode(:);
+ err = ones(k,1) * err;
+ err = err(:);
+ cerr = ones(n,1) * cerr;
+ cerr = cerr(:);
+ else
+ err = err(:);
+ cerr = cerr(:);
+ if (strcmp(msgtyp,"decimal"))
+ msg = bi2de(msg);
+ ccode = bi2de(ccode);
+ endif
+ endif
+
+endfunction
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