Related papers: Correction to "The Generalized Stochastic Likeliho…
This paper has been withdrawn by the author, due a crucial error in the proof of the main Theorem (Sec. 3). In particular, in deriving the bound on the probability of error (Eq. 10) the contribution of those pairs (x', y') that are not…
Correction to Annals of Probability 28 (2000) 277--302 [doi:10.1214/aop/1019160120].
We show that for a wide range of channels and code ensembles with pairwise-independent codewords, with probability tending to 1 with the code length, expurgating an arbitrarily small fraction of codewords from a randomly selected code…
The aim of this short note is to fill in a gap in our earlier paper [16] on 2BSDEs with reflections, and to explain how to correct the subsequent results in the second paper [15]. We also provide more insight on the properties of 2RBSDEs,…
In the literature there exists analytical expressions for the probability of a receiver decoding a transmitted source message that has been encoded using random linear network coding. In this work, we look into the probability that the…
We give the proof of a tight lower bound on the probability that a binomial random variable exceeds its expected value. The inequality plays an important role in a variety of contexts, including the analysis of relative deviation bounds in…
The distributed hypothesis testing problem with full side-information is studied. The trade-off (reliability function) between the two types of error exponents under limited rate is studied in the following way. First, the problem is…
We analyze the list-decodability, and related notions, of random linear codes. This has been studied extensively before: there are many different parameter regimes and many different variants. Previous works have used complementary styles…
Correction to "Limit theorems for coupled continuous time random walks" (Ann. Probab. 32 (2004) 730-756).
We correct some oversights in the paper "A spectral sequence for stratified spaces and configuration spaces of points" by the second named author. In particular we explain that an additional hypothesis should be added to Theorem 4.15 in…
We correct a small gap found in the authors' paper 'On bounds for the effective differential Nullstellensatz' (J Algebra 449:1-21, 2016). This gap is due to an inequality that does not generally hold. However, under one additional…
We initiate the probabilistic analysis of linear programming (LP) decoding of low-density parity-check (LDPC) codes. Specifically, we show that for a random LDPC code ensemble, the linear programming decoder of Feldman et al. succeeds in…
In this paper q-ary Raptor codes under ML decoding are considered. An upper bound on the probability of decoding failure is derived using the weight enumerator of the outer code, or its expected weight enumerator if the outer code is drawn…
We prove the following results concerning the list decoding of error-correcting codes: (i) We show that for \textit{any} code with a relative distance of $\delta$ (over a large enough alphabet), the following result holds for \textit{random…
The purpose of this note is to point to a gap in an argument in our paper "Stabilization for the automorphisms of free groups with boundaries", and explain how to fill it.
There has been a great deal of work establishing that random linear codes are as list-decodable as uniformly random codes, in the sense that a random linear binary code of rate $1 - H(p) - \epsilon$ is $(p,O(1/\epsilon))$-list-decodable…
The purpose of this article is to point out a mistake in the published paper "Graphs of hyperbolic groups and limit set intersection theorem- Proc AMS, vol 146, no 5, pp 1859--1871, which subsequently weakens the main theorem of that paper.…
We correct the proofs of the main theorems in our paper "Limit theorems for Betti numbers of random simplicial complexes".
The likelihood encoder with a random codebook is demonstrated as an effective tool for source coding. Coupled with a soft covering lemma (associated with channel resolvability), likelihood encoders yield simple achievability proofs for…
In the present contribution we establish quantitative results on the periodic approximation of the corrector equation for the stochastic homogenization of linear elliptic equations in divergence form, when the diffusion coefficients satisfy…