Thread: error correction

can anyone help me in studying error correction especially reed solomon coding

what i need is the algorithym and the implementation in application ( writing a code in any language)

Reed-Solomon Codes

An introduction to Reed-Solomon codes: principles, architecture and implementation

1. Introduction

Reed-Solomon codes are block-based error correcting codes with a wide range of applications in digital communications and storage. Reed-Solomon codes are used to correct errors in many systems including:

Storage devices (including tape, Compact Disk, DVD, barcodes, etc)
Wireless or mobile communications (including cellular telephones, microwave links, etc)
Satellite communications
Digital television / DVB
High-speed modems such as ADSL, xDSL, etc.
A typical system is shown here:



The Reed-Solomon encoder takes a block of digital data and adds extra "redundant" bits. Errors occur during transmission or storage for a number of reasons (for example noise or interference, scratches on a CD, etc). The Reed-Solomon decoder processes each block and attempts to correct errors and recover the original data. The number and type of errors that can be corrected depends on the characteristics of the Reed-Solomon code.

2. Properties of Reed-Solomon codes

Reed Solomon codes are a subset of BCH codes and are linear block codes. A Reed-Solomon code is specified as RS(n,k) with s-bit symbols.

This means that the encoder takes k data symbols of s bits each and adds parity symbols to make an n symbol codeword. There are n-k parity symbols of s bits each. A Reed-Solomon decoder can correct up to t symbols that contain errors in a codeword, where 2t = n-k.

The following diagram shows a typical Reed-Solomon codeword (this is known as a Systematic code because the data is left unchanged and the parity symbols are appended):


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