Reed-solomon system and problem

Reed-Solomon (RS) codes are widely employed for error correction due to its distinct capability of correcting both random and burst errors.Complexity of RS encoder and decoder increases with the error correcting capability of the codes.The code is very much suited from VLSI design viewpoint and requires more hardware and power for decoding is high.This leads to the design of CA based Codec. 

One weakness of the Reed-solomon system is that single byte error in mth information byte and double byte errors (one in mth information byte and another in the last information byte) correspond to same equation for error location identification.This System can correct errors provided errors are confined to information or check byte only. The system cannot correct if the errors are distributed both in information and check bytes.

Mode Of Implementation.

ModelSim 6.3c is used for programming as well as simulation. VHDL is considered as primary language and For Synthesis the tool used is XILINX ISE 10.1.

Syndrome Generator

Syndrome generator block involves calculation of check bytes at  the receiver side for the  received data.
The computed check bytes are compared with the check bytes of the encoder scheme.The expression is  Si=eCi xor dCi
eCi-encoded check byte
dCi-decode check byte
i-check byte number.
if  S value is a zero element then no error exists.
If  S value is non zero then an error has occurred in I th byte.
Check byte computation in encoder and decoder are the same

Cellular Automata Decoder

A Decoder is the exact opposite to that of an "Encoder". It is basically, a combinational type logic circuit that converts the binary code data at its  input into one of a number of different output lines, one at a time producing an  equivalent decimal code at its output. 

CA based decoder consists of  4 blocks:
1.Syndrome  generator
2.Error location identifier
3.Error magnitude identifier
4.Error correction block

Introduction

CA(Cellular Automata) consist of a number of cells arranged in a regular manner, where the state transitions of each cell depends on the state of its neighbors.Each cell consists of D flip-flop and a combinational logic implementing the next-state function. The next state function is called the rule of the automata.In this we can detect and correct errors presented in different systems.