Related papers: Correction to "The Generalized Stochastic Likeliho…
The likelihood decoder is a stochastic decoder that selects the decoded message at random, using the posterior distribution of the true underlying message given the channel output. In this work, we study a generalized version of this…
This paper studies random-coding error exponents of randomised list decoding, in which the decoder randomly selects $L$ messages with probabilities proportional to the decoding metric of the codewords. The exponents (or bounds) are given…
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…
This is a corrected version of our paper published in Osaka Journal of Mathematics 51(2014), 673-693. We correct Theorem~1.1, Proposition~3.3 and their proofs.
A Lagrange-dual (Gallager-style) lower bound is derived for the error exponent function of the typical random code (TRC) pertaining to the i.i.d. random coding ensemble and mismatched stochastic likelihood decoding. While the original…
A gap in the proof of Theorem 3.5 in the paper ``A new iteration process for approximation of common fixed points for finite families of total asymtotically nonexpansive mappings". Int. J. Math. Math. Sci. vol. 2009,…
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…
This work studies the deviations of the error exponent of the constant composition code ensemble around its expectation, known as the error exponent of the typical random code (TRC). In particular, it is shown that the probability of…
We close a gap appearing at the same time in the author's thesis "Iterated rings of bounded elements and generalizations of Schm\"udgen's theorem" [1] and in the author's article "Iterated rings of bounded elements and generalizations of…
This article corrects two mistakes in the article "Coarse homology theories" [math.AT/0106183].
In 1973, Gallager proved that the random-coding bound is exponentially tight for the random code ensemble at all rates, even below expurgation. This result explained that the random-coding exponent does not achieve the expurgation exponent…
Lower and upper bounds are explored for the uniform (Kolmogorov) and $L^2$-distances between the distributions of weighted sums of dependent summands and the normal law. The results are illustrated for several classes of random variables…
An elementary proof of the attainability of random coding exponent with linear codes for additive channels is presented. The result and proof are from Hamada (Proc. ITW, Chendu, China, 2006), and the present material explains the proof in…
An upper bound on the error probability of specific lattices, based on their distance-spectrum, is constructed. The derivation is accomplished using a simple alternative to the Minkowski-Hlawka mean-value theorem of the geometry of numbers.…
There is a gap in Theorem 2.2 of the paper of Du (\cite{D_2010}). In this paper, we shall state the gap and repair it.
Random linear codes are a workhorse in coding theory, and are used to show the existence of codes with the best known or even near-optimal trade-offs in many noise models. However, they have little structure besides linearity, and are not…
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…
Statistical physics is employed to evaluate the performance of error-correcting codes in the case of finite message length for an ensemble of Gallager's error correcting codes. We follow Gallager's approach of upper-bounding the average…
This paper presents an achievability bound that evaluates the exact probability of error of an ensemble of random codes that are decoded by a minimum distance decoder. Compared to the state-of-the-art which demands exponential computation…
In the note an error in Low and Lapsley's article ("Optimization Flow Control, I: Basic Algorithm and Convergence", IEEE/ACM Transactions on Networking, 7(6), pp. 861-874, 1999) is pointed out. Because of this error the proof of the Theorem…