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rmdemap.m
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rmdemap.m
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function [decodedMessage] = rmdemap(y,r,m)
% function [decodedMessage] = rmdemap(y,r,m)
%
% RMDEC_REED demaps an RM(r,m) codeword using Reed's algorithm by means of polynomial evaluation.
%
% Source: [1] Reed-Muller Codes: Theory and Algorithms by Emmanuel Abbe, Amir
% Shpilka and Min Ye, 2020.
% [2] Reed-Muller Codes, Sebastian Raaphorst, Carleton University, 2003.
%
% Written by Yuval Ben-Hur, 05/03/2020
%
if ~isequal(size(y),[2^m,1]) && ~isequal(size(y),[1,2^m])
error('Invalid input size.');
end
if ~all(y==1 | y==0)
error('Only binary RM supported.');
end
y = y(:).';
Z = de2bi(2^m-1:-1:0,'right-msb').';
[~,AscendingOrder] = sort(sum(Z,1),'ascend');
Z_ = Z(:,AscendingOrder);
Z_r = Z_(:,sum(Z_,1)<=r);
kRM = size(Z_r,2);
decodedMessage = zeros(1,kRM); % initialize decoded message
for ii = kRM : -1 : 1
% define monom
A = find(Z_r(:,ii)); % monom variables
t = numel(A); % monom rank
% define cosets
if t==0 % A is the empty set {}
z = 1 : m;
logic = mode(y(z)); % decoded bit is majority of logic
elseif t==m % A is the full set {1,...,m}
logic = mod(sum(y),2);
else
b = de2bi(0,m-t,'right-msb').';
% sum over a coset
z = all(Z(setdiff(1:m,A),:) == b,1);
logic = mod(sum(y(z)),2);
end
decodedMessage(ii) = logic;
% if next rank is different, reduce monomials of previous rank
if ii==1 || numel(find(Z_r(:,ii-1)))<t
y = mod(y - rmenc_v2(decodedMessage.*(sum(Z_r,1)==t),r,m),2);
end
end