rsenc

Reed-Solomon encoder

Syntax

code = rsenc(msg,n,k)
code = rsenc(msg,n,k,genpoly)
code = rsenc(...,paritypos)


Description

code = rsenc(msg,n,k) encodes the message in msg using an [n,k] Reed-Solomon code with the narrow-sense generator polynomial. msg is a Galois array of symbols having m bits each. Each k-element row of msg represents a message word, where the leftmost symbol is the most significant symbol. n is at most 2^m-1. If n is not exactly 2^m-1, rsenc uses a shortened Reed-Solomon code. Parity symbols are at the end of each word in the output Galois array code.

code = rsenc(msg,n,k,genpoly) is the same as the syntax above, except that a nonempty value of genpoly specifies the generator polynomial for the code. In this case, genpoly is a Galois row vector that lists the coefficients, in order of descending powers, of the generator polynomial. The generator polynomial must have degree n-k. To use the default narrow-sense generator polynomial, set genpoly to [].

code = rsenc(...,paritypos) specifies whether rsenc appends or prepends the parity symbols to the input message to form code. paritypos can be either 'end' or 'beginning'. The default is 'end'.

Examples

Reed-Solomon Code Generation

Set the code parameters.

m = 3;           % Number of bits per symbol
n = 2^m - 1;     % Codeword length 
k = 3;           % Message length

Create two messages based on GF(8).

msg = gf([2 7 3; 4 0 6],m)

 
msg = GF(2^3) array. Primitive polynomial = D^3+D+1 (11 decimal)
 
Array elements = 
 
   2   7   3
   4   0   6

Generate RS (7,3) codewords.

code = rsenc(msg,n,k)

 
code = GF(2^3) array. Primitive polynomial = D^3+D+1 (11 decimal)
 
Array elements = 
 
   2   7   3   3   6   7   6
   4   0   6   4   2   2   0

The codes are systematic so the first three symbols of each row match the rows of msg.

Limitations

n and k must differ by an integer. n between 7 and 65535.

Version History

Introduced before R2006a