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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.


Papers
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Journal ArticleDOI
TL;DR: In this paper, an adaptive SC-List decoder for polar codes with CRC was proposed, which iteratively increases the list size until at least one survival path can pass CRC.
Abstract: In this letter, we propose an adaptive SC (Successive Cancellation)-List decoder for polar codes with CRC. This adaptive SC-List decoder iteratively increases the list size until at least one survival path can pass CRC. Simulation shows that the adaptive SC-List decoder provides significant complexity reduction. We also demonstrate that polar code (2048, 1024) with 24-bit CRC decoded by our proposed adaptive SC-List decoder with very large maximum list size can achieve a frame error rate FER ≤ 10-3{-3} at Eb/No = 1.1dB, which is about 0.25dB from the information theoretic limit at this block length.

316 citations

Journal ArticleDOI
TL;DR: It is shown that for even codes the set of zero neighbors is strictly optimal in this class of algorithms, which implies that general asymptotic improvements of the zero-neighbors algorithm in the frame of gradient-like approach are impossible.
Abstract: Minimal vectors in linear codes arise in numerous applications, particularly, in constructing decoding algorithms and studying linear secret sharing schemes. However, properties and structure of minimal vectors have been largely unknown. We prove basic properties of minimal vectors in general linear codes. Then we characterize minimal vectors of a given weight and compute their number in several classes of codes, including the Hamming codes and second-order Reed-Muller codes. Further, we extend the concept of minimal vectors to codes over rings and compute them for several examples. Turning to applications, we introduce a general gradient-like decoding algorithm of which minimal-vectors decoding is an example. The complexity of minimal-vectors decoding for long codes is determined by the size of the set of minimal vectors. Therefore, we compute this size for long randomly chosen codes. Another example of algorithms in this class is given by zero-neighbors decoding. We discuss relations between the two decoding methods. In particular, we show that for even codes the set of zero neighbors is strictly optimal in this class of algorithms. This also implies that general asymptotic improvements of the zero-neighbors algorithm in the frame of gradient-like approach are impossible. We also discuss a link to secret-sharing schemes.

313 citations

Proceedings ArticleDOI
06 Jul 2001
TL;DR: This paper compares the speed and output quality of a traditional stack-based decoding algorithm with two new decoders: a fast greedy decoder and a slow but optimal decoder that treats decoding as an integer-programming optimization problem.
Abstract: A good decoding algorithm is critical to the success of any statistical machine translation system. The decoder's job is to find the translation that is most likely according to set of previously learned parameters (and a formula for combining them). Since the space of possible translations is extremely large, typical decoding algorithms are only able to examine a portion of it, thus risking to miss good solutions. In this paper, we compare the speed and output quality of a traditional stack-based decoding algorithm with two new decoders: a fast greedy decoder and a slow but optimal decoder that treats decoding as an integer-programming optimization problem.

300 citations

Journal ArticleDOI
TL;DR: A modification of the Fincke-Pohst (sphere decoding) algorithm to estimate the maximum a posteriori probability of the received symbol sequence is proposed and, over a wide range of rates and signal-to-noise ratios, has polynomial-time complexity.
Abstract: In recent years, soft iterative decoding techniques have been shown to greatly improve the bit error rate performance of various communication systems. For multiantenna systems employing space-time codes, however, it is not clear what is the best way to obtain the soft information required of the iterative scheme with low complexity. In this paper, we propose a modification of the Fincke-Pohst (sphere decoding) algorithm to estimate the maximum a posteriori probability of the received symbol sequence. The new algorithm solves a nonlinear integer least squares problem and, over a wide range of rates and signal-to-noise ratios, has polynomial-time complexity. Performance of the algorithm, combined with convolutional, turbo, and low-density parity check codes, is demonstrated on several multiantenna channels. The results for systems that employ space-time modulation schemes seem to indicate that the best performing schemes are those that support the highest mutual information between the transmitted and received signals, rather than the best diversity gain.

298 citations

Book ChapterDOI
15 Apr 2012
TL;DR: The ball collision technique of Bernstein, Lange and Peters was used to reduce the complexity of Stern's information set decoding algorithm to 20.0556n by as mentioned in this paper, and this bound was improved by May, Meurer and Thomae.
Abstract: Decoding random linear codes is a well studied problem with many applications in complexity theory and cryptography. The security of almost all coding and LPN/LWE-based schemes relies on the assumption that it is hard to decode random linear codes. Recently, there has been progress in improving the running time of the best decoding algorithms for binary random codes. The ball collision technique of Bernstein, Lange and Peters lowered the complexity of Stern's information set decoding algorithm to 20.0556n. Using representations this bound was improved to 20.0537n by May, Meurer and Thomae. We show how to further increase the number of representations and propose a new information set decoding algorithm with running time 20.0494n.

295 citations


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