Matched Metrics and Channels

Firer, Marcelo; Walker, Judy L.

doi:10.1109/tit.2015.2512596

Cited by 19 publications

(29 citation statements)

References 9 publications

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“…it is a direct consequence of Equation (4) in Section V. The metrizability of BAC n (p, q) was established in [4] for the case pq = 0 and n arbitrary (the n-fold Z-channel) and for p + q < 1 and n = 2, 3. The remaining case is when p + q < 1 and pq > 0.…”

Section: Preliminariesmentioning

confidence: 95%

“…A channel W : X → X is metrizable (in the strong sense of [4] and [3]) if there is a metric d : X × X → [0, ∞) (i.e. d is a definite-positive symmetric function satisfying the triangle inequality) such that every nearest neighbor decoder is a maximum likelihood decoder and vice versa.…”

Section: Preliminariesmentioning

confidence: 99%

“…Thus, the graph G 1 (W) has 8 edges and it is represented in Figure 1. A sufficient condition to guarantee the non-existence of a metric matched to a given channel W is given in Proposition 5 of [4]. This condition states that if the channel W : X → X admits a decision chain of length r ≥ 3 it is not metrizable.…”

Section: The Graph G 1 Associated With a Channelmentioning

confidence: 99%

“…The case pq = 0 corresponds to the Z-channels which we know they are metrizable (Theorem 6 of [4]), then we can assume pq > 0. Each entry of its transition matrix M n (p, q) is of the form…”

Section: The Bac Channel Is Metrizablementioning

confidence: 99%

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Matched Metrics to the Binary Asymmetric Channels

Qureshi

2019

IEEE Trans. Inform. Theory

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In this paper we establish some criteria to decide when a discrete memoryless channel admits a metric in such a way that the maximum likelihood decoding coincides with the nearest neighbor decoding. In particular we prove a conjecture presented by M. Firer and J. L. Walker establishing that every binary asymmetric channel admits a matched metric. Index TermsBinary asymmetric channel, channel model, maximum likelihood decoding I. INTRODUCTIONAs it is well known, maximum likelihood decoding (MLD) over a symmetric channel coincides with nearest neighbor decoding (NND) with respect to the Hamming metric. In this paper we deal with the problem of matching a metric to a given channel regarding the decoding criteria mentioned above. This problem was considered in 1967 by J. L. Massey [2] where a metric matched to a discrete memoryless channel is defined as a metric for which the NND is a MLD.Since then, this type of matching have been studied in some special cases. For instance, certain channels matching to the Lee metric were obtained in [1]. The problem of matching a metric to a channel was taken up by G. Séguin [3], where the main focus was on sequences of additive metrics. In the referred paper it is used a stronger condition also assumed here: a metric matched to a channel is one for which not only the NND is a MLD but also the MLD is a NND. The

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Section: Preliminariesmentioning

confidence: 95%

Section: Preliminariesmentioning

confidence: 99%

Section: The Graph G 1 Associated With a Channelmentioning

confidence: 99%

Section: The Bac Channel Is Metrizablementioning

confidence: 99%

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Matched Metrics to the Binary Asymmetric Channels

Qureshi

2019

IEEE Trans. Inform. Theory

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“…Consider a BAC with transition probabilities p, q ∈ [0, 1] 2 . A BAC is reasonable (in the sense of [18]) if their transition probabilities verify Pr(0|0) > Pr(0|1) and Pr(1|1) > Pr(1|0). Note that this is equivalent to the condition p + q < 1.…”

Section: Further Remarks a On The Bac-function And The Parametermentioning

confidence: 99%

On Equivalence of Binary Asymmetric Channels Regarding the Maximum Likelihood Decoding

Qureshi

Costa

Rodrigues

et al. 2018

IEEE Trans. Inform. Theory

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We study the problem of characterizing when two memoryless binary asymmetric channels, described by their transition probabilities (p, q) and (p , q ), are equivalent from the point of view of maximum likelihood decoding (MLD) when restricted to n-block binary codes. This equivalence of channels induces a partition (depending on n) on the space of parameters (p, q) into regions associated with the equivalence classes. Explicit expressions for describing these regions, their number and areas are derived. Some perspectives of applications of our results to decoding problems are also presented. Index TermsBinary memoryless channel, binary asymmetric channel, maximum likelihood decoding, mismatched decoding

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