Sequential decoding

About: Sequential decoding is a research topic. Over the lifetime, 8667 publications have been published within this topic receiving 204271 citations.

Analysis of Low-Density Parity-Check Codes Based on EXIT Functions

Abstract: We exploit extrinsic information transfer functions of single parity-check and repetition codes over the binary input additive white Gaussian noise (biAWGN) channel, derived by the authors, for asymptotic performance analysis of belief propagation decoding of low-density parity-check codes. The approach is based on a Gaussian approximation (GA) of the density evolution algorithm using the mutual information measure. We show that this method allows more accurate prediction of the decoding threshold in the biAWGN channel than the earlier known GA methods

Iterative reliability-based decoding of linear block codes with adaptive belief propagation

Abstract: In this letter, an iterative decoding algorithm for linear block codes combining reliability-based decoding with adaptive belief propagation decoding is proposed. At each iteration, the soft output values delivered by the adaptive belief propagation algorithm are used as reliability values to perform reduced order reliability-based decoding of the code considered. This approach allows to bridge the gap between the error performance achieved by the lower order reliability-based decoding algorithms which remain sub-optimum, and the maximum likelihood decoding, which is too complex to be implemented for most codes employed in practice. Simulations results for various linear block codes are given and elaborated.

Random Redundant Soft-In Soft-Out Decoding of Linear Block Codes

Abstract: A number of authors have recently considered iterative soft-in soft-out (SISO) decoding algorithms for classical linear block codes that utilize redundant Tanner graphs. Jiang and Narayanan presented a practically realizable algorithm that applies only to cyclic codes while Kothiyal et al. presented an algorithm that, while applicable to arbitrary linear block codes, does not imply a low-complexity implementation. This work first presents the aforementioned algorithms in a common framework and then presents a related algorithm - random redundant iterative decoding - that is both practically realizable and applicable to arbitrary linear block codes. Simulation results illustrate the successful application of the random redundant iterative decoding algorithm to the extended binary Golay code. Additionally, the proposed algorithm is shown to outperform Jiang and Narayanan's algorithm for a number of Bose-Chaudhuri-Hocquenghem (BCH) codes

List decoding of generalized reed-solomon codes by using a modified extended key equation algorithm

Abstract: This work presents a modified extended key equation algorithm in list decoding of generalized Reed-Solomon (GRS) codes. A list decoding algorithmof generalized Reed-Solomon codes has two steps, interpolation and factorization. The extended key equation algorithm (EKE) is an interpolation-based approach with a lower complexity than Sudan's algorithm. To increase the decoding speed, this work proposes a modified EKE algorithm to perform codeword checking prior to such an interpolation process. Since the evaluation mapping is engaged in encoding, a codeword is not generated systematically. Thus, the transmission information is not directly obtained from a received codeword. Therefore, the proposed algorithm undertakes a matrix operation to obtain the transmission information once a received vector has been checked to be error-free. Simulation results demonstrate that the modified EKE algorithm in list decoding of a GRS code provides low complexity, particularly at high signal-to-noise ratios.

Coding Theory: Algorithms, Architectures and Applications

Abstract: Preface. 1 Introduction. 1.1 Communication Systems. 1.2 Information Theory. 1.2.1 Entropy. 1.2.2 Channel Capacity. 1.2.3 Binary Symmetric Channel. 1.2.4 AWGN Channel. 1.3 A Simple Channel Code. 2 Algebraic Coding Theory. 2.1 Fundamentals of Block Codes. 2.1.1 Code Parameters. 2.1.2 Maximum Likelihood Decoding. 2.1.3 Binary Symmetric Channel. 2.1.4 Error Detection and Error Correction. 2.2 Linear Block Codes. 2.2.1 Definition of Linear Block Codes. 2.2.2 Generator Matrix. 2.2.3 Parity Check Matrix. 2.2.4 Syndrome and Cosets. 2.2.5 Dual Code. 2.2.6 Bounds for Linear Block Codes. 2.2.7 Code Constructions. 2.2.8 Examples of Linear Block Codes. 2.3 Cyclic Codes. 2.3.1 Definition of Cyclic Codes. 2.3.2 Generator Polynomial. 2.3.3 Parity Check Polynomial. 2.3.4 Dual Codes. 2.3.5 Linear Feedback Shift Registers. 2.3.6 BCH Codes. 2.3.7 Reed-Solomon Codes. 2.3.8 Algebraic Decoding Algorithm. 2.4 Summary. 3 Convolutional Codes. 3.1 Encoding of Convolutional Codes. 3.1.1 Convolutional Encoder. 3.1.2 Generator Matrix in Time-Domain. 3.1.3 State Diagram of a Convolutional Encoder. 3.1.4 Code Termination. 3.1.5 Puncturing. 3.1.6 Generator Matrix in D -Domain. 3.1.7 Encoder Properties. 3.2 Trellis Diagram and Viterbi's Algorithm. 3.2.1 Minimum Distance Decoding. 3.2.2 Trellises. 3.2.3 Viterbi Algorithm. 3.3 Distance Properties and Error Bounds. 3.3.1 Free Distance. 3.3.2 Active Distances. 3.3.3 Weight Enumerators for Terminated Codes. 3.3.4 Path Enumerators. 3.3.5 Pairwise Error Probability. 3.3.6 Viterbi Bound. 3.4 Soft Input Decoding. 3.4.1 Euclidean Metric. 3.4.2 Support of Punctured Codes. 3.4.3 Implementation Issues. 3.5 Soft Output Decoding. 3.5.1 Derivation of APP Decoding. 3.5.2 APP Decoding in the Log-Domain. 3.6 Convolutional Coding in Mobile Communications. 3.6.1 Coding of Speech Data. 3.6.2 Hybrid ARQ. 3.6.3 EGPRS Modulation and Coding. 3.6.4 Retransmission Mechanism. 3.6.5 Link Adaptation. 3.6.6 Incremental Redundancy. 3.7 Summary. 4 Turbo Codes. 4.1 LDPC Codes. 4.1.1 Codes Based on Sparse Graphs. 4.1.2 Decoding for the Binary Erasure Channel. 4.1.3 Log-Likelihood Algebra. 4.1.4 Belief Propagation. 4.2 A First Encounter with Code Concatenation. 4.2.1 Product Codes. 4.2.2 Iterative Decoding of Product Codes. 4.3 Concatenated Convolutional Codes. 4.3.1 Parallel Concatenation. 4.3.2 The UMTS Turbo Code. 4.3.3 Serial Concatenation. 4.3.4 Partial Concatenation. 4.3.5 Turbo Decoding. 4.4 EXIT Charts. 4.4.1 Calculating an EXIT Chart. 4.4.2 Interpretation. 4.5 Weight Distribution. 4.5.1 Partial Weights. 4.5.2 ExpectedWeight Distribution. 4.6 Woven Convolutional Codes. 4.6.1 Encoding Schemes. 4.6.2 Distance Properties of Woven Codes. 4.6.3 Woven Turbo Codes. 4.6.4 Interleaver Design. 4.7 Summary. 5 Space-Time Codes. 5.1 Introduction. 5.1.1 Digital Modulation Schemes. 5.1.2 Diversity. 5.2 Spatial Channels. 5.2.1 Basic Description. 5.2.2 Spatial Channel Models. 5.2.3 Channel Estimation. 5.3 Performance Measures. 5.3.1 Channel Capacity. 5.3.2 Outage Probability and Outage Capacity. 5.3.3 Ergodic Error Probability. 5.4 Orthogonal Space-Time Block Codes. 5.4.1 Alamouti's Scheme. 5.4.2 Extension to more than two Transmit Antennas. 5.4.3 Simulation Results. 5.5 Spatial Multiplexing. 5.5.1 General Concept. 5.5.2 Iterative APP Preprocessing and Per-Layer Decoding. 5.5.3 Linear Multi-Layer Detection. 5.5.4 Original Bell Labs Layered Space Time (BLAST) Detection. 5.5.5 QL Decomposition and Interference Cancellation. 5.5.6 Performance of Multi-Layer Detection Schemes. 5.5.7 Unified Description by Linear Dispersion Codes. 5.6 Summary. A. Algebraic Structures. A.1 Groups, Rings and Finite Fields. A.1.1 Groups. A.1.2 Rings. A.1.3 Finite Fields. A.2 Vector Spaces. A.3 Polynomials and Extension Fields. A.4 Discrete Fourier Transform. B. Linear Algebra. C. Acronyms. Bibliography . Index.