Coding for Informed Decoders

12/11/01

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Table of Contents

Coding for Informed Decoders

System Aspects of Error Correction

Block Codes for Error Correction

The Systematic [7,4] Hamming Code

Coding for Informed Decoders

Example: Systematic [7,4,3] Hamming Code

Geometric view of classical code

Geometric view of what we want

General Concept for Linear Codes

Informed Decoder Distance

Making the subcodes stronger than the parent code

Picking a better Generator Matrix

Reed Solomon Codes

Reed Solomon Codes

ID-RS based on Nested Subcodes

ID-RS based on Nested Subcodes

Decoding such ID-RS Codes

Another ID-RS Code Construction

Intermezzo on error and erasure correction

ID-RS based on Code Puncturing

Decoding such Punctured Codes

[12,7,6] ID-RS Code & Hamming Distance

Coding Gains of Informed Decoder @ 10-12

General results for Reed-Solomon-like codes

ID-RS based on Nested Subcodes

Encoding & Information Extraction

Decoding such ID-RS codes

Properties of the [12,7,6] ID-Code over F16

Structure of the [12,7,6] ID-Code over F16

Structure of the [12,7,6] ID-Code (cont.)

Decoding a classical [12,7,6] RS Code

Decoding the [12,7,6] ID-Code

Decoding the [12,7,6] ID-Code (cont.)

An Encoder for the [12,7,6] ID-Code

Performance Analysis & Complexity of Coding for Informed Decoders for DVR

Definitions of Error rate

Performance Computations (Gaussian Noise)

Conclusions on decoding performance

Author: COS