Topic
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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TL;DR: A wide class of low-density parity-check codes is introduced, large enough to include LDPC codes over finite fields, rings, or groups, as well as some nonlinear codes.
Abstract: We introduce a wide class of low-density parity-check (LDPC) codes, large enough to include LDPC codes over finite fields, rings, or groups, as well as some nonlinear codes. A belief-propagation decoding procedure with the same complexity as for the decoding of LDPC codes over finite fields is also presented. Moreover, an encoding procedure is developed
64 citations
TL;DR: It is shown that the coding scheme achieves the capacity region of noiseless WOMs when an arbitrary number of multiple writes is permitted and the results can be generalized from binary to generalized WOMs, described by an arbitrary directed acyclic graph.
Abstract: A coding scheme for write once memory (WOM) using polar codes is presented. It is shown that the scheme achieves the capacity region of noiseless WOMs when an arbitrary number of multiple writes is permitted. The encoding and decoding complexities scale as O(N log N), where N is the blocklength. For N sufficiently large, the error probability decreases subexponentially in N. The results can be generalized from binary to generalized WOMs, described by an arbitrary directed acyclic graph, using nonbinary polar codes. In the derivation, we also obtain results on the typical distortion of polar codes for lossy source coding. Some simulation results with finite length codes are presented.
64 citations
TL;DR: An upper bound on the maximal transmission rate over binary-input memoryless channels, provided that the decoding decision rule is given, is derived and if the decisionRule is equivalent to the maximum-likelihood decoding, then the bound coincides with the channel capacity.
Abstract: An upper bound on the maximal transmission rate over binary-input memoryless channels, provided that the decoding decision rule is given, is derived. If the decision rule is equivalent to the maximum-likelihood decoding (matched decoding), then the bound coincides with the channel capacity. Otherwise (mismatched decoding), it coincides with a known lower bound.
64 citations
TL;DR: This article gives a tutorial introduction to research on the iterative decoding of state-of-the-art error correcting codes such as turbo codes, and it is estimated that analog decoder can outperform digital decoders by two orders of magnitude in speed and/or power consumption.
Abstract: The iterative decoding of state-of-the-art error correcting codes such as turbo codes is computationally demanding. It is argued that analog implementations of such decoders can be much more efficient than digital implementations. This article gives a tutorial introduction to research on this topic. It is estimated that analog decoders can outperform digital decoders by two orders of magnitude in speed and/or power consumption.
63 citations
Dissertation•
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01 Jan 2007
TL;DR: This thesis is devoted to one such algorithm - Bidirectional Efficient Algorithm for Searching code Trees, known as BEAST-APP decoding, which is applied as soft-input soft-output detector for transmission over intersymbol interference channels.
Abstract: Modern communication systems are designed to enable reliable and fast information transfer. Therefore, efficient channel coding and decoding strategies are needed, which guarantee sufficiently low probability of erroneous reception with affordable receiver complexity. For many channel codes, optimal decoding with traditional methods is prohibitively complex. The challenge therefore lies in designing reduced-complexity decoding algorithms that achieve optimal or near-optimal performance. This thesis is devoted to one such algorithm - Bidirectional Efficient Algorithm for Searching code Trees. The taming of the BEAST is laid out in several steps. After an introduction to coding, trellis and tree representations of codes are reviewed as prerequisites for understanding the BEAST. Maximum-likelihood decoding using BEAST, and its generalization to list decoding are presented first. An investigation of geometrical aspects of list decoding has resulted in new bounds on the list error probability. It is shown that the performance of a list decoder is determined by the worst-case list configuration, which yields the minimum list distance of a code. A commonly used approach for achieving a good performance/complexity tradeoff is to use concatenated codes with iterative decoding, where decoders of constituent codes, employed as separate entities, iteratively exchange information on decoded symbols. In such a setup, the decoders provide soft symbol reliabilities in the form of a posteriori probabilities (APPs). It is shown that accurate APP approximations can be obtained from a short list of the most probable codewords found by BEAST. This decoding method is referred to as BEAST-APP decoding. Product codes belong to the class of iteratively decodable codes and the BEAST-APP decoder is used for decoding of constituent codes, yielding good performance with low complexity. Finally, BEAST is applied as soft-input soft-output detector for transmission over intersymbol interference channels. Its advantages and limitations in comparison to existing decoding methods are discussed. (Less)
63 citations