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Embedding Distances into the Hamming Cube

Abstract : In Coding Theory, two different decision criteria types are mostly used: a maximal likelihood (relative to a probabilistic model of a channel) and a nearest neighbour criterion (relative to a distance model of the channel). In this work we present an algorithm that, given a maximal likelihood criterion, decides if there is a nearest neighbour criterion that matches it and, in this case, produces a metric that determines such a criterion. It is also shown that the Hamming metric is universal, in the sense that any metric, up to a decoding equivalence, can be isometrically embedded into a hypercube with the Hamming metric.
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https://hal.inria.fr/hal-01276469
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Submitted on : Friday, February 19, 2016 - 2:19:48 PM
Last modification on : Monday, February 22, 2016 - 11:26:14 AM
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Rafael d'Oliveira, Marcelo Firer. Embedding Distances into the Hamming Cube. The 9th International Workshop on Coding and Cryptography 2015 WCC2015, Anne Canteaut, Gaëtan Leurent, Maria Naya-Plasencia, Apr 2015, Paris, France. ⟨hal-01276469⟩

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