# Unit information: Coding Theory (M) in 2019/20

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Unit name Coding Theory (M) EENGM2010 10 M/7 Teaching Block 1 (weeks 1 - 12) Professor. Piechocki Not open None None Department of Electrical & Electronic Engineering Faculty of Engineering

## Description

Coding theory tackles the theory and design of error correction codes. Error correction codes are a common component within many communications and data storage systems, to ensure that information is accurately reproduced in the presence of transmission errors. The codes rely on the addition of additional redundant parity data in order to facilitate the detection and correction of transmission errors.

The subject stems from pioneering work by Claude Shannon in 1948 who showed that it is theoretically possible to accurately transmit data at any rate below the channel capacity. Since then much effort has been invested in the development of good codes and efficient decoding methods for reliable communication. Many of the commonly used techniques rely on the use of the structure associated with finite algebra.

This module will cover a variety of commonly used coding techniques including linear block codes, cyclic codes and convolutional codes. The performance of codes will be examined, both for random errors, burst errors and time varying or fading channels. The module will also cover other practically useful techniques, including interleaving, Reed Solomon codes, product codes, concatenated codes, turbo codes and other iteratively decoded codes.

Elements:

• Introduction to Coding Theory - Shannon’s noisy coding theorem, channel types, code rate , coding gain;
• Block codes - encoding and decoding, Hamming distance;
• Finite algebra; - finite fields, vector spaces;
• Linear block codes - generator and parity check matrices, systematic codes, standard array, performance bounds, Hamming codes, modified codes, calculation of error rates;
• Cyclic codes - generator polynomials, syndrome calculation, modified codes, low rate codes, CRCs, Reed Solomon codes;
• Convolutional codes - encoding, state & trellis diagrams, Viterbi decoding, performance, puncturing for code adaptation;
• Practical exercise – implementing and simulating linear block codes in Matlab, comparing theoretical performance for block codes.

## Intended learning outcomes

On completion of this unit the student will be able to:

1. Outline the problems and techniques used for error correction coding.
2. Apply the theory behind many of the codes, taking into account the importance of linearity, and the use of finite algebra.
3. Explain in detail linear block codes including encoding and decoding techniques, coding bounds, theoretical performance and coding gain.
4. Explain in detail cyclic codes including encoding and decoding techniques.
5. Outline non-binary codes including Reed Solomon codes.
6. Explain in detail both non-recursive and recursive convolutional codes including encoding, Viterbi decoding and puncturing for adaptive performance.
7. Describe compound codes including product codes and concatenated codes.
8. Outline, at system level, iterative decoding techniques and their application to turbo codes, product codes, LDPC and turbo equalization.
9. Implement and simulate codes using Matlab.

## Teaching details

Lectures and laboratory work

## Assessment Details

1. Technical report on laboratory work, 20% (ILO 9)
2. Exam, 2 hours, 80% (ILOs 1-8)