Reed solomon Code for encoder and decoder

% Reed-Solomon coding based on the test vectors presented in
% IEEE Std 802.16-2004


%% Input vector x and output vector z taken from Sect. 8.3.3.5.1, p444

x = ['D4';'BA';'A1';'12';'F2';'74';'96';'30'; ...
     '27';'D4';'88';'9C';'96';'E3';'A9';'52'; ...
     'B3';'15';'AB';'FD';'92';'53';'07';'32'; ...
     'C0';'62';'48';'F0';'19';'22';'E0';'91'; ...
     '62';'1A';'C1'];

z = ['49';'31';'40';'BF';'D4';'BA';'A1';'12'; ...
     'F2';'74';'96';'30';'27';'D4';'88';'9C'; ...
     '96';'E3';'A9';'52';'B3';'15';'AB';'FD'; ...
     '92';'53';'07';'32';'C0';'62';'48';'F0'; ...
     '19';'22';'E0';'91';'62';'1A';'C1';'00'];

x = hex2dec(x)'; % This is the input data from the standard
z = hex2dec(z)'; % This how the output data should be

% Note that the parity bytes are first four bytes in the vector z, namely
% '49';'31';'40';'BF' (hex).


%% Define Reed-Solomon coding parameters 
m = 8; % Number of bits per symbol
n = 2^m-1; % Length of encoded data (255 for m=8)
k = 239; % Required length of source data (ie RS(255,239) )
t= (n-k)/2;

%% Define the field generator primitive polynomial (D^8+D^4+D^3+D^2+1)
% in decimal form according to eqn.(67), p432.
p = 285; 

%% Form the msg vector from the input data. If the input data is shorter
%  than required, prefix it with zeros.
Nzeros = k-length(x)-1; % Calculate how much zero padding to add.
xk=[zeros(1,Nzeros) x 0]; % Make source data. Prefix with zero pads if needed.

%% Creat Galois array from the source data
msg=gf(xk, m, p);

% Calculate the code generator polynomial according to eqn.(66) on p432 
% of the standard (note that the 4th argument is 0 in the function call)
% Expanding eqn.(66) gives the following polynomial coefficients:
% 1 59 13 104 189 68 209 30 8 163 65 41 229 98 50 36 59
gen=rsgenpoly(n, k, p, 0);

%% Encode the message
code = rsenc(msg,n,k,gen);
% Note that Octave does not appear to place the parity bytes where expected so some
% sorting is required.

code_new = [code(k+1:k+(t/2)) code(Nzeros+1:k)];