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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Pascale Charpin, Nicolas Sendrier, Jean-Pierre Tillich. The 9th International Workshop on Coding and Cryptography 2015 WCC2015, Apr 2015, Paris, France. 2016, Proceedings of the 9th International Workshop on Coding and Cryptography 2015 WCC2015. 〈wcc2015.inria.fr〉
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Rafael D'Oliveira, Marcelo Firer. Embedding Distances into the Hamming Cube. Pascale Charpin, Nicolas Sendrier, Jean-Pierre Tillich. The 9th International Workshop on Coding and Cryptography 2015 WCC2015, Apr 2015, Paris, France. 2016, Proceedings of the 9th International Workshop on Coding and Cryptography 2015 WCC2015. 〈wcc2015.inria.fr〉. 〈hal-01276469〉

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