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IEEE Transactions on Information Theory
Article . 1979 . Peer-reviewed
License: IEEE Copyright
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image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
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Replication decoding

Authors: M. Decouvelaere; G. Battail; Philippe Godlewski;

Replication decoding

Abstract

Any symbol in a redundant code can be recovered when it belongs to certain erasure patterns. Several alternative expressions of a given symbol, to be referred to as its replicas, can therefore be computed in terms of other ones. Decoding is interpreted as decoding upon a received symbol, given itself and a number of such replicas, expressed in terms of other received symbols. For linear q-ary (n,k) block codes, soft-decision demodulation and memoryless channels, the maximum-likelihood decision rule on a given symbol is formulated in terms of r \leqn - k linearly independent replicas from the parity-check equations. All replicas deriving from the r selected replicas by linear combination are actually taken into account in this decision rule. Its implementation can be direct; use transformations or a sequential circuit implementing a trellis representation of the parity-check matrix. If r = n - k , decoding is optimum, in the sense of symbol-by-symbol maximum-likelihoed. Simplification results in the transformed and sequential implementations when r . If the selected replicas are disjoint, generalized ( q -ary, weighted) threshold decoding results. The decoding process can easily be modffied in order to provide word-by-word maximum-likelihood decoding. Convolutional codes are briefly considered. Two specific problems are discussed: the use of previous decisions, which leads to a weighted generalization of feedback decoding, and the extension of replication decoding to nonsystematic codes.

Related Organizations
Keywords

Communication System, Redundant Codes, Decoding, Linear Codes, Symbol-By-Symbol Maximum Likelihood Decision, Convolutional Codes, Convolutional codes, Replication Decoding

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
81
Top 10%
Top 0.1%
Average
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