Related papers: Parameters of Codes for the Binary Asymmetric Chan…
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 address the problem of bounding below the probability of error under maximum likelihood decoding of a binary code with a known distance distribution used on a binary symmetric channel. An improved upper bound is given for the maximum…
The binary asymmetric channel is a model for practical communication systems where the error probabilities for symbol transitions $0\rightarrow 1$ and $1\rightarrow0$ differ substantially. In this paper, we introduce the notion of…
In this letter, we analyse the properties of a maximum likelihood channel estimator based on the syndrome of a linear code. For the two examples of a binary symmetric channel and a binary input additive white Gaussian noise channel, we…
This paper introduces techniques to construct binary polar source/channel codes based on the bit error probability of successive-cancellation decoding. The polarization lemma is reconstructed based on the bit error probability and then…
A linear-programming decoder for \emph{nonbinary} expander codes is presented. It is shown that the proposed decoder has the maximum-likelihood certificate properties. It is also shown that this decoder corrects any pattern of errors of a…
This work contains two main contributions concerning the asymmetric broadcast channel. The first is an analysis of the exact random coding error exponents for both users, and the second is the derivation of universal decoders for both…
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 performance of maximum-likelihood (ML) decoded binary linear block codes is addressed via the derivation of tightened upper bounds on their decoding error probability. The upper bounds on the block and bit error probabilities are valid…
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…
We derive critical noise levels for Gallager codes on asymmetric channels as a function of the input bias and the temperature. Using a statistical mechanics approach we study the space of codewords and the entropy in the various decoding…
We compare the performance of short-length linear binary codes on the binary erasure channel and the binary-input Gaussian channel. We use a universal decoder that can decode any linear binary block code: Gaussian-elimination based…
The problem of blind identification of channel codes at a receiver involves identifying a code chosen by a transmitter from a known code-family, by observing the transmitted codewords through the channel. Most existing approaches for…
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…
A new lower bound on the error probability of maximum likelihood decoding of a binary code on a binary symmetric channel was proved in Barg and McGregor (2004, cs.IT/0407011). It was observed in that paper that this bound leads to a new…
In this paper, we consider quantized decoding of LDPC codes on the binary symmetric channel. The binary message passing algorithms, while allowing extremely fast hardware implementation, are not very attractive from the perspective of…
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 neighbour decoding. In particular we prove a conjecture…
We consider communication over binary-input memoryless output-symmetric channels using low-density parity-check codes and message-passing decoding. The asymptotic (in the length) performance of such a combination for a fixed number of…
We study the channel coding problem when errors and uncertainty occur in the encoding process. For simplicity we assume the channel between the encoder and the decoder is perfect. Focusing on linear block codes, we model the encoding…
Function-correcting codes are a class of codes designed to protect the function evaluation of a message against errors whose key advantage is the reduced redundancy. In this paper, we extend function-correcting codes from binary symmetric…