Synopses & Reviews
Error correcting coding is often analyzed in terms of its application to the separate levels within the data network in isolation from each other. In this fresh approach, the authors consider the data network as a superchannel
(a multi-layered entity) which allows error correcting coding to be evaluated as it is applied to a number of network layers as a whole. By exposing the problems of applying error correcting coding in data networks, and by discussing coding theory and its applications, this original technique shows how to correct errors in the network through joint
coding at different network layers.
- Discusses the problem of reconciling coding applied to different layers using a superchannel approach
- Includes thorough coverage of all the key codes: linear block codes, Hamming, BCH and Reed-Solomon codes, LDPC codes decoding, as well as convolutional, turbo and iterative coding
- Considers new areas of application of error correcting codes such as transport coding, code-based cryptosystems and coding for image compression
- Demonstrates how to use error correcting coding to control such important data characteristics as mean message delay
- Provides theoretical explanations backed up by numerous real-world examples and practical recommendations
- Features a companion website containing additional research results including new constructions of LDPC codes, joint error-control coding and synchronization, Reed-Muller codes and their list decoding
By progressing from theory through to practical problem solving, this resource contains invaluable advice for researchers, postgraduate students, engineers and computer scientists interested in data communications and applications of coding theory.
"…a comprehensive view of error coding theory and explores its use and implementation at all network layers…" (Computing Reviews.com, February 1, 2006)
In this new approach, the authors consider the data network as a channel (in the sense of information theory) with several layers. The suggested global approach to coding in a network is consequently connected with other network procedures, such as protocols, and this determines complexity and originality of the problems of coding within the network. The authors distinguish different coding processes at 3 network layers (data link layer, transport layer and presentation layer) and investigate the impact of coding from one layer to another. Thus the problem of reconciliation of coding of different network layers arises and the authors suggest enlightening solutions to this problem.
The book consists of two parts:
PART 1 is mainly devoted to a review of coding theory and its applications. This part differs from the traditional monographs available on coding theory, as it focuses on nonbinary codes and the correction of special configurations of errors, dictated by a class of problems.
PART 2 discusses how to solve the problems raised in part 1 and is the main focus of the book. It shows how, with the help of coding which adds redundant packets to the message, it is possible to decrease the mean time of message delivery and increase the probability of not exceeding the acceptable delay limit. Methods of construction of a model of the discrete data channel and choice of the code for the data channel are presented. Many problems, considered in this part, have significance not only for data networks, but also for other sections of the communication theory.
Table of Contents
1 Problems Facing Error Control Coding in Data Networks.
1.1 International Recommendations on Using Error Control Coding at Different Network Layers.
1.2 Classification of Problems on Coding in Networks.
2 Block Codes.
2.1 Main Definitions.
2.2 Algebraic Structures.
2.3 Linear Block Codes.
2.4 Cyclic Codes.
2.5 Bounds on Minimum Distance.
3 General Methods of Decoding of Linear Codes.
3.1 Minimum Distance Decoding.
3.2 Information Set Decoding.
3.3 A Supercode Decoding Algorithm.
3.4 The Complexity of Decoding in the Channel with Independent Errors.
4 Codes with Algebraic Decoding.
4.1 Hamming Codes.
4.2 Reed-Solomon Codes.
4.3 BCH Codes.
4.4 Decoding of BCH Codes.
4.5 The Sudan Algorithm and its Extensions.
5 Decoding of LDPC Codes.
5.1 Low-Density Parity-Check Codes.
5.2 LDPC Constructions.
5.3 Estimating the Minimum Distance of EG-LDPC Codes.
5.4 Burst-Error-Correcting LDPC Codes.
5.5 Decoding Schemes of LDPC Codes.
5.6 Simulation Results in AWGN.
Appendix 5.A Euclidean Geometries.
6 Convolutional Codes and Turbo-Codes.
6.1 Convolutional Codes Representation and Encoding.
6.2 Viterbi Decoding Algorithm.
6.3 List Decoding.
6.4 Sequential Decoding.
6.5 Parallel-Concatenated Convolutional Codes and Soft Input Soft Output Decoding.
6.6 SISO Decoding Algorithms.
7 Coding of Messages at the Transport Layer of the Data Network.
7.1 Decreasing the Message Delay with the help of Transport Coding.
7.2 Transmission of Message during Limited Time.
7.3 Transmission of Priority Messages without using Priority Packets .
7.4 Estimation of the Effectiveness of Transport Coding for the Nonexponential Model of Packet Delay.
8 Providing Security of Data in a Network with the Help of Coding Methods.
8.1 Public-Key Cryptography.
8.2 Codebased Cryptosystems: McEliece and Niederreiter.
8.3 Cryptosystems Based on Full Decoding.
8.4 Further Development of Codebased Cryptosystems.
8.5 Codebased Cryptosystems and RSA: Comparison and Perspectives.
8.6 Codebased Signature.
9 Reconciliation of Coding at Different Layers of a Network.
9.1 Transport Coding in a Network with Unreliable Channels.
9.2 Reconciliation of Channel and Transport Coding.
9.3 Use of Tornado Codes for Reconciliation of Channel and Transport Coding.
9.4 Development of Coding Methods at the Presentation Layer.
9.5 Reconciliation of Coding at Neighbour Layers of a Network.