scispace - formally typeset
Search or ask a question
Topic

List decoding

About: List decoding is a research topic. Over the lifetime, 7251 publications have been published within this topic receiving 151182 citations.


Papers
More filters
Journal ArticleDOI
TL;DR: In this article, it was shown that maximum likelihood decoding of Reed-Solomon codes is NP-hard even with unlimited preprocessing, thus strengthening a result of Bruck and Naor.
Abstract: Maximum-likelihood decoding is one of the central algorithmic problems in coding theory. It has been known for over 25 years that maximum-likelihood decoding of general linear codes is NP-hard. Nevertheless, it was so far unknown whether maximum-likelihood decoding remains hard for any specific family of codes with nontrivial algebraic structure. In this paper, we prove that maximum-likelihood decoding is NP-hard for the family of Reed-Solomon codes. We moreover show that maximum-likelihood decoding of Reed-Solomon codes remains hard even with unlimited preprocessing, thereby strengthening a result of Bruck and Naor.

91 citations

Journal ArticleDOI
TL;DR: This paper presents two low-complexity reliability-based message-passing algorithms for decoding LDPC codes over non-binary finite fields that provide effective trade-off between error performance and decoding complexity compared to the non- binary sum product algorithm.
Abstract: This paper presents two low-complexity reliability-based message-passing algorithms for decoding LDPC codes over non-binary finite fields. These two decoding algorithms require only finite field and integer operations and they provide effective trade-off between error performance and decoding complexity compared to the non-binary sum product algorithm. They are particularly effective for decoding LDPC codes constructed based on finite geometries and finite fields.

90 citations

Journal ArticleDOI
TL;DR: The concept of combining the design of the error-correcting-coding approach and the modulation format is treated in general terms and its effectiveness is demonstrated by a specific implementation referred to as Codem I.
Abstract: The concept of combining the design of the error-correcting-coding approach and the modulation format is treated in general terms and its effectiveness is demonstrated by a specific implementation referred to as Codem I. A new decoding algorithm is presented, which has the interesting property that the only channel measurement information utilized is the relative reliability of each received digit. The effectiveness of this decoding technique is demonstrated by computer simulation over three different channel models for dispersive channels. Comparisons of the performance of Codem I with the more conventional 16-tone (four-phase DPSK) HF modem are obtained by actual field results as well as by computer simulations. Improvement in error probability in the region of two orders of magnitude is demonstrated when both systems are operating under similar channel conditions and at equal data rates. A further improvement is demonstrated when channel measurement information is used to reject a small percentage (typically less than 3 percent) of codewords that are considered unreliable.

90 citations

Journal ArticleDOI
TL;DR: It is proved that a random linear code over $\mathbb{F}_q, with probability arbitrarily close to 1, is list decodable at radius $1-1/q-\epsilon$ with list size and rate and the desired average-distance guarantees hold.
Abstract: We prove that a random linear code over $\mathbb{F}_q$, with probability arbitrarily close to 1, is list decodable at radius $1-1/q-\epsilon$ with list size $L=O(1/\epsilon^2)$ and rate $R=\Omega_q(\epsilon^2/(\log^3(1/\epsilon)))$. Up to the polylogarithmic factor in $1/\epsilon$ and constant factors depending on $q$, this matches the lower bound $L=\Omega_q(1/\epsilon^2)$ for the list size and upper bound $R=O_q(\epsilon^2)$ for the rate. Previously only existence (and not abundance) of such codes was known for the special case $q=2$ (Guruswami et al., 2002). In order to obtain our result, we employ a relaxed version of the well-known Johnson bound on list decoding that translates the average Hamming distance between codewords to list decoding guarantees. We furthermore prove that the desired average-distance guarantees hold for a code provided that a natural complex matrix encoding the codewords satisfies the restricted isometry property with respect to the Euclidean norm. For the case of random binary...

90 citations

Proceedings ArticleDOI
04 Aug 2003
TL;DR: The main computational steps in algebraic soft decoding, as well as Sudan-type list decoding, of Reed-Solomon codes are interpolation and factorization, and a series of transformations are given for the interpolation problem that arises in these decoding algorithms.
Abstract: The main computational steps in algebraic soft decoding, as well as Sudan-type list decoding, of Reed-Solomon codes are interpolation and factorization. A series of transformations is given for the interpolation problem that arises in these decoding algorithms. These transformations reduce the space and time complexity to a small fraction of the complexity of the original interpolation problem. A factorization procedure that applies directly to the reduced interpolation problem is also presented.

89 citations


Network Information
Related Topics (5)
Base station
85.8K papers, 1M citations
89% related
Fading
55.4K papers, 1M citations
89% related
Wireless network
122.5K papers, 2.1M citations
87% related
Network packet
159.7K papers, 2.2M citations
87% related
Wireless
133.4K papers, 1.9M citations
86% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202384
2022153
202179
202078
201982
201894