How to generate error correction using Reed-Solomon Encoder?

I make QR code encoding which use Reed-Solomon encoding for error correction, I want to make 26 blocks codeword, contains 13 blocks message, and 13 blocks error correction. each block is decimal from 8 bit binary. I'm try using examples from help below:

n = 255; k = 13; % Codeword length and message length n=(2^m)-1

m = 8; % Number of bits in each symbol

msg = [32 91 11 120 209 114 220 77 67 64 236 17 236]; % Message is a Galois array.

obj = comm.RSEncoder(n, k);

c1 = step(obj, msg);

the output is 255 blocks, it can't be change value of n become 26;

then I try to using shortened message Reed solomon part III from help example below:

 shortenLength = 229;

>> % Create a (63,53) RS encoder System object, and an RS decoder with an

>> % erasures input port, and two punctures.

>> N = 255;  % Codeword length

>> K = 242;  % Message length

>> numErasures = 8;

>> numPuncs = 2;

>> hEnc = comm.RSEncoder('BitInput', false);

hDec = comm.RSDecoder('BitInput', false, 'ErasuresInputPort', true);

hEnc.PuncturePatternSource = 'Property';

>> hEnc.PuncturePattern = [ones(N-K-numPuncs,1); zeros(numPuncs,1)];

>> hDec.PuncturePatternSource = 'Property';

>> hDec.PuncturePattern = hEnc.PuncturePattern;

>> % Set the shortened codeword length and message length values

>> hEnc.CodewordLength = N - shortenLength;

>> hEnc.MessageLength = K - shortenLength;

>> hDec.CodewordLength = N - shortenLength;

>> hDec.MessageLength = K - shortenLength;

>> hEnc.CodewordLength = N - shortenLength;

>> hEnc.CodewordLength

ans =

      26

>> hEnc.PrimitivePolynomialSource = 'Property';

>> hEnc.PrimitivePolynomial = de2bi(primpoly(6, 'nodisplay'), 'left-msb');

hDec.PrimitivePolynomialSource = 'Property';

hDec.PrimitivePolynomial = de2bi(primpoly(6, 'nodisplay'), 'left-msb');

I got N and K value for 26 and 13 like I want, but I didn't get error correction from that function, anyone already using this Reed Solomon encoding?

[Vuxyom]

Hi I have exactly the same problem, if you find the solution can you tell me. Thank's

Answer 1

[Thach Bui]

You should do some maths before programming. For example, the following code produces the message length of S in the field 2^7.

N = 127;  % Codeword length
K = 5;  % Message length
S = K; % shortened message length
m = log2(N + 1); % field GF(2^m)

%numErasures = 8;
numPuncs = N - K;

rsEncoder = comm.RSEncoder(N, K, 'BitInput', false);
rsEncoder.PuncturePatternSource = 'Property';
rsEncoder.PuncturePattern = [ones(N-K-numPuncs,1); zeros(numPuncs,1)];

% Set the shortened message length values
rsEncoder.ShortMessageLength = S;

% Specify the field of GF(2^6) in the RS encoder/decoder System objects, by setting the PrimitivePolynomialSource property ...
% to 'Property' and the PrimitivePolynomial property to a 6th degree primitive polynomial.
rsEncoder.PrimitivePolynomialSource = 'Property';
rsEncoder.PrimitivePolynomial = de2bi(primpoly(m, 'nodisplay'), 'left-msb');

%%Encoding process
  % Data symbols - transmit 1 message word at a time, each message word has S symbols in the [0 2^P-1] range. P is the degree of the
  % primitive polynomial specified in the RS encoder/decoder, which in this example equals 6.
  data = randi([0 2^m-1], S, 1);

   % Encode the shortened message word. The encoded word encData is N-numPuncs-K+S symbols long.
    encData = step(rsEncoder, data);