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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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Journal ArticleDOI
TL;DR: Simulation of finite length instances of the proposed mixed-kernels construction scheme indicate their advantages both in error correction performance and complexity compared to the known polar coding structures.
Abstract: Mixed kernels of polar codes are mapping functions having inputs of different alphabet sizes that are used to construct polar coding scheme. These schemes are constructed by incorporating several (homogeneous) kernels, each one over different alphabet size. In this paper, the idea of mixed-kernels construction is introduced and analyzed. An asymptotic analysis of the proposed scheme shows that its polarization properties are strongly related to the ones of the constituent kernels. Simulation of finite length instances of the scheme indicate their advantages both in error correction performance and complexity compared to the known polar coding structures.

52 citations

Journal ArticleDOI
L. Lee1
TL;DR: It is shown that the new algorithm offers advantages over Viterbi decoding in soft-decision applications, such as in the inner coding system for concatenated coding.
Abstract: A recursive procedure is derived for decoding of rate R = 1/n binary convolutional codes which minimizes the probability of the individual decoding decisions for each information bit, subject to the constraint that the decoding delay be limited to Δ branches. This new decoding algorithm is similar to, but somewhat more complex than, the Viterbi decoding algorithm. A "real-time," i.e., fixed decoding delay, version of the Viterbi algorithm is also developed and used for comparison to the new algorithm on simulated channels. It is shown that the new algorithm offers advantages over Viterbi decoding in soft-decision applications, such as in the inner coding system for concatenated coding.

52 citations

Patent
20 Jul 2012
TL;DR: In this article, a Reed-Solomon (RS) error-correction system is described, where a decision-codeword corresponds to an inner code and an RS code is the outer code.
Abstract: Systems and methods are provided for implementing various aspects of a Reed-Solomon (RS) error-correction system. A detector can provide a decision-codeword from a channel and can also provide soft-information for the decision-codeword. If the decision-codeword corresponds to an inner code and an RS code is the outer code, a soft-information map can process the soft-information for the decision-codeword to produce soft-information for a RS decision-codeword. A RS decoder can employ the Berlekamp-Massey algorithm (BMA), list decoding, and a Chien search, and can include a pipelined architecture. A threshold-based control circuit can be used to predict whether list decoding will be needed and can suspend the list decoding operation if it predicts that list decoding is not needed.

52 citations

Book
31 Oct 2002
TL;DR: This text discusses codes for low-Density Parity-Check Codes, Convolutional Encoding, and the Elements of Graph Theory, which describes the construction of rings, Domains, and Fields in sets and groups.
Abstract: List of Figures. List of Tables. Preface. 1: Digital Communication. 1. Basics. 2. Algorithms and Complexity. 3. Encoding and Decoding. 4. Bounds. 5. Overview of the Text. 2: Abstract Algebra. 1. Sets and Groups. 2. Rings, Domains, and Fields. 3. Vector Spaces and GF(pm). 4. Polynomials over Galois Fields. 5. Frequency Domain Analysis of Polynomials over GF(q) [x]/(xn-1). Linear Block Codes. 1. Basic Structure of Linear Codes. 2. Repetition and Parity Check Codes. 3. Hamming Codes. 4. Reed-Muller Codes. 5. Cyclic Codes. 6. Quadratic Residue Codes. 7. Golay Codes. 8. BCH and Reed-Solomon Codes. 4: Convolutional and Concatenated Codes. 1. Convolutional Encoders. 2. Analysis of Component Codes. 3. Concatenated Codes. 4. Analysis of Parallel Concatenated Codes. 5: Elements of Graph Theory. 1. Introduction. 2. Martingales. 3. Expansion. 6: Algorithms on Graphs. 1. Probability Models and Bayesian Networks. 2. Belief Propagation Algorithm. 3. Junction Tree Propagation Algorithm. 4. Message Passing and Error Control Decoding. 5. Message Passing in Loops. 7: Turbo Decoding. 1. Turbo Decoding. 2. Parallel Decoding. 3. Notes. 8: Low-Density Parity-Check Codes. 1. Basic Properties. 2. Simple Decoding Algorithms. 3. Explicit Construction. 4. Gallager's Decoding Algorithms. 5. Belief Propagation Decoding. 6. Notes. 9: Low-Density Generator Codes. 1. Introduction. 2. Decoding Analyses. 3. Good Degree Sequences. 4. Irregular Repeat-Accumulate Codes. 5. Cascaded Codes. 6. Notes. References. Index.

51 citations

Journal ArticleDOI
TL;DR: This brief study studies the application of a similar technique to a class of Euclidean geometry low density parity check (EG-LDPC) codes that are one step majority logic decodable and shows that the method is also effective for EG- LDPC codes.
Abstract: In a recent paper, a method was proposed to accelerate the majority logic decoding of difference set low density parity check codes. This is useful as majority logic decoding can be implemented serially with simple hardware but requires a large decoding time. For memory applications, this increases the memory access time. The method detects whether a word has errors in the first iterations of majority logic decoding, and when there are no errors the decoding ends without completing the rest of the iterations. Since most words in a memory will be error-free, the average decoding time is greatly reduced. In this brief, we study the application of a similar technique to a class of Euclidean geometry low density parity check (EG-LDPC) codes that are one step majority logic decodable. The results obtained show that the method is also effective for EG-LDPC codes. Extensive simulation results are given to accurately estimate the probability of error detection for different code sizes and numbers of errors.

51 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202384
2022153
202179
202078
201982
201894