Error Correcting Coding and Security for Data Networks

Grigorii Kabatiansky is the author of Error Correcting Coding and Security for Data Networks: Analysis of the Superchannel Concept, published by Wiley. Professor Evgenii Krouk has worked in the field of communication theory and techniques for more than 30 years. His areas of interests are coding theory, the mathematical theory of communications and cryptography. He is now the Dean of the Information Systems and Data Protection Faculty of the Saint-Petersburg State University of Aerospace Instrumentation. He is author of 3 books, more than 100 scientific articles and 30 international and Russian patents. Sergei Semenov received his Ph.D. degree from St.-Petersburg State University for Airspace Instrumentation (SUAI), Russia in 1993. Dr. Semenov joined Nokia Corporation in 1999 and is currently a Specialist in Modem Algorithm Design/Wireless Modem. His research interests include coding and communication theory and their application to communication systems.

Preface. 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.

Index.