Related papers: Tightened Upper Bounds on the ML Decoding Error Pr…
In practice, since many communication networks are huge in scale, or complicated in structure, or even dynamic, the predesigned linear network codes based on the network topology is impossible even if the topological structure is known.…
This paper studies maximum likelihood(ML) decoding in error-correcting codes as rational maps and proposes an approximate ML decoding rule by using a Taylor expansion. The point for the Taylor expansion, which will be denoted by $p$ in the…
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…
In this paper, we develop a new decoding algorithm of a binary linear codes for symbol-pair read channels. Symbol-pair read channel has recently been introduced by Cassuto and Blaum to model channels with high write resolution but low read…
The question whether RM codes are capacity-achieving is a long-standing open problem in coding theory that was recently answered in the affirmative for transmission over erasure channels [1], [2]. Remarkably, the proof does not rely on…
Spinal codes, a family of rateless codes introduced in 2011, have been proved to achieve Shannon capacity over both the additive white Gaussian noise (AWGN) channel and the binary symmetric channel (BSC). In this paper, we derive explicit…
A new algorithm for efficient exact maximum likelihood decoding of polar codes (which may be CRC augmented), transmitted over the binary erasure channel, is presented. The algorithm applies a matrix triangulation process on a sparse polar…
We investigate threshold-based multi-trial decoding of concatenated codes with an inner Maximum-Likelihood decoder and an outer error/erasure (L+1)/L-extended Bounded Distance decoder, i.e. a decoder which corrects e errors and t erasures…
As the mobile application landscape expands, wireless networks are tasked with supporting various connection profiles, including real-time communications and delay-sensitive traffic. Among many ensuing engineering challenges is the need to…
This paper studies the performance of block coding on an additive white Gaussian noise channel under different power limitations at the transmitter. Lower bounds are presented for the minimum error probability of codes satisfying maximal…
Some new results are derived concerning random coding error exponents and expurgated exponents for list decoding with a deterministic list size $L$. Two asymptotic regimes are considered, the fixed list-size regime, where $L$ is fixed…
In this paper, we propose a new upper bound on the error probability performance of maximum-likelihood (ML) detection. The proposed approach provides a much tighter upper bound when compared to the traditionally used union bound, especially…
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…
In this paper, we derive analytic expressions for the success probability of decoding (Partial) Unit Memory codes in memoryless channels. An applications of this result is that these codes outperform individual block codes in certain…
We present Kovalenko's full-rank limit as a tight lower bound for decoding error probability of LDPC codes and LT codes over BEC. From the limit, we derive a full-rank overhead as a lower bound for stable overheads for successful…
This work contains two main contributions concerning the expurgation of hierarchical ensembles for the asymmetric broadcast channel. The first is an analysis of the optimal maximum likelihood (ML) decoders for the weak and strong user. Two…
A new property which relies on the linear programming (LP) decoder, the approximate maximum-likelihood certificate (AMLC), is introduced. When using the belief propagation decoder, this property is a measure of how close the decoded…
We develop a framework for linear-programming (LP) decoding of non-binary linear codes over rings. We prove that the resulting LP decoder has the `maximum likelihood certificate' property, and we show that the decoder output is the lowest…
It is shown that some well-known and some new cyclic codes with orthogonal parity-check equations can be constructed in the finite-field transform domain. It is also shown that, for some binary linear cyclic codes, the performance of the…
An approach is established for maximizing the Lower bound on the Mismatch capacity (hereafter abbreviated as LM rate), a key performance bound in mismatched decoding, by optimizing the channel input probability distribution. Under a fixed…