Related papers: Matched Metrics to the Binary Asymmetric Channels

The most common decision criteria for decoding are maximum likelihood decoding and nearest neighbor decoding. It is well-known that maximum likelihood decoding coincides with nearest neighbor decoding with respect to the Hamming metric on…

We present an algorithm that, given a channel, determines if there is a distance for it such that the maximum likelihood decoder coincides with the minimum distance decoder. We also show that any metric, up to a decoding equivalence, can be…

We introduce two notions of discrepancy between binary vectors, which are not metric functions in general but nonetheless capture the mathematical structure of the binary asymmetric channel. In turn, these lead to two new fundamental…

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…

Independent parallel q-ary symmetric channels are a suitable transmission model for several applications. The proposed weighted-Hamming metric is tailored to this setting and enables optimal decoding performance. We show that some…

In this paper, we study the symmetry of polar codes on symmetric binary-input discrete memoryless channels (B-DMC). The symmetry property of polar codes is originally pointed out in Arikan's work for general B-DMC channels. With the…

Two channels are equivalent if their maximum likelihood (ML) decoders coincide for every code. We show that this equivalence relation partitions the space of channels into a generalized hyperplane arrangement. With this, we define a coding…

The quantization of the output of a binary-input discrete memoryless channel to a smaller number of levels is considered. An algorithm which finds an optimal quantizer, in the sense of maximizing mutual information between the channel input…

This paper investigates achievable information rates and error exponents of mismatched decoding when the channel belongs to the class of channels that are close to the decoding metric in terms of relative entropy. For both discrete- and…

The error probability of block codes sent under a non-uniform input distribution over the memoryless binary symmetric channel (BSC) and decoded via the maximum a posteriori (MAP) decoding rule is investigated. It is proved that the ratio of…

We consider the discrete memoryless asymmetric broadcast channels. We prove that the error probability of decoding tends to one exponentially for rates outside the capacity region and derive an explicit lower bound of this exponent…

This paper studies the mismatched decoding problem for binary-input discrete memoryless channels. An example is provided for which an achievable rate based on superposition coding exceeds the LM rate (Hui, 1983; Csisz\'ar-K\"orner, 1981),…

Over discrete memoryless channels (DMC), linear decoders (maximizing additive metrics) afford several nice properties. In particular, if suitable encoders are employed, the use of decoding algorithm with manageable complexities is…

The Poltyrev bound provides a very tight upper bound on the decoding error probability when using binary linear codes for transmission over the binary symmetric channel and the additive white Gaussian noise channel, making use of the code's…

For the class of the memoryless binary-input channels which are not necessarily symmetric, we derive tight bounds on the capacity in terms of the Bhattacharyya parameter. As it turns out, the bounds derived under the symmetric channel…

This paper considers the performance of Reed-Muller (RM) codes transmitted over binary memoryless symmetric (BMS) channels under bitwise maximum-a-posteriori (bit-MAP) decoding. Its main result is that, for a fixed BMS channel, the family…

This paper studies channel coding for the discrete memoryless multiple-access channel with a given (possibly suboptimal) decoding rule. A multi-letter successive decoding rule depending on an arbitrary non-negative decoding metric is…

We address the problem of correcting a single error in an arbitrary discrete memoryless channel with error-free instantaneous feedback. For the case of a one-time feedback, we propose a method for constructing optimal transmission…

Over binary input channels, uniform distribution is a universal prior, in the sense that it allows to maximize the worst case mutual information over all binary input channels, ensuring at least 94.2% of the capacity. In this paper, we…

In this paper we analyze the probabilistic matching of sources with memory to channels with memory so that symbol-by-symbol code with memory without anticipation are optimal, with respect to an average distortion and excess distortion…