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List decoding
About: List decoding is a research topic. Over the lifetime, 7251 publications have been published within this topic receiving 151182 citations.
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08 Jul 2010
TL;DR: A survey of Reed-Muller (RM) coding is given with the goal of establishing a continuity between RM codes and polar codes.
Abstract: A survey of Reed-Muller (RM) coding is given with the goal of establishing a continuity between RM codes and polar codes. The focus is mainly on recursive decoding methods for RM codes and other ideas that are most relevant to polar coding.
66 citations
24 Jun 2007
TL;DR: It is shown that both recoverability and minimum decoding overhead of any MPG code with MR property depend only on the configuration, where decoding overhead is defined as the additional number of symbols to access, in order to decode the lost data symbols.
Abstract: In this paper, we study the maximally recoverable (MR) property for multi-protection group (MPG) codes. MPG codes with MR property achieve the best erasure recoverability given configurations, where a configuration represents the structural relationship between data and parity symbols. We present construction and decoding algorithms for MPG codes with MR property. We show that both recoverability and minimum decoding overhead of any MPG code with MR property depend only on the configuration, where decoding overhead is defined as the additional number of symbols to access, in order to decode the lost data symbols.
66 citations
TL;DR: Shannon's zero-error channel capacities C/sub OF/C/sub O/ with and without noiseless feedback are generalized to list decoding: the receiver lists L messages, erring if the correct one is not listed.
Abstract: Shannon's zero-error channel capacities C/sub OF/, C/sub O/ with and without noiseless feedback are generalized to list decoding: the receiver lists L messages, erring if the correct one is not listed. The corresponding capacities C/sub OF/(L), C/sub O/(L) are nondecreasing in L. For an I-letter input alphabet, C/sub OF/(L) attains its maximum at L=I-1. A lower bound to C/sub O/(L) approaches that maximum as L increases. >
66 citations
Book•
10 Dec 2007
TL;DR: In this article, the authors present a classification of problems on Coding in networks and propose a solution to overcome these problems using error control codes at different layers of the network, including linear block codes and cyclic codes.
Abstract: 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.
66 citations
TL;DR: A modified algorithm for decoding of low-density parity-check codes over finite-state binary Markov channels that outperforms systems in which the channel statistics are not exploited in the decoding, even when the channel parameters are not known a priori at the decoder.
Abstract: We propose a modified algorithm for decoding of low-density parity-check codes over finite-state binary Markov channels. The proposed approach clearly outperforms systems in which the channel statistics are not exploited in the decoding, even when the channel parameters are not known a priori at the decoder.
66 citations