Related papers: Optimal list decoding from noisy entropy inequalit…
We study encodings that give the best known thresholds for the non-zero capacity of quantum channels, i.e., the upper bound for correctable noise, using an entropic approach to calculation of the threshold values. Our results show that…
This paper is devoted to the finite-length analysis of turbo decoding over the binary erasure channel (BEC). The performance of iterative belief-propagation (BP) decoding of low-density parity-check (LDPC) codes over the BEC can be…
Motivated by recent studies of population coding in theoretical neuroscience, we examine the optimality of a recently described form of stochastic resonance known as suprathreshold stochastic resonance, which occurs in populations of noisy…
In this work, we consider the problem of efficient decoding of codes from insertions and deletions. Most of the known efficient codes are codes with synchronization strings which allow one to reduce the problem of decoding insertions and…
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…
Polar encoding, described by Arikan in IEEE Transactions on Information Theory, Vol. 55, No. 7, July 2009, was a milestone for telecommunications. A Polar code distributes information among high and low-capacity channels, showing the…
Maximum entropy models are increasingly being used to describe the collective activity of neural populations with measured mean neural activities and pairwise correlations, but the full space of probability distributions consistent with…
Recently, Samorodnitsky proved a strengthened version of Mrs. Gerber's Lemma, where the output entropy of a binary symmetric channel is bounded in terms of the average entropy of the input projected on a random subset of coordinates. Here,…
In this paper, by treating Reed-Muller (RM) codes as a special class of low-density parity-check (LDPC) codes and assuming that sub-blocks of the parity-check matrix are randomly interleaved to each other as Gallager's codes, we present a…
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 capacity of a channel with an energy-harvesting (EH) encoder and a finite battery remains an open problem, even in the noiseless case. A key instance of this scenario is the binary EH channel (BEHC), where the encoder has a unit-sized…
We present a new information-theoretic definition and associated results, based on list decoding in a source coding setting. We begin by presenting list-source codes, which naturally map a key length (entropy) to list size. We then show…
Error exponents characterize the exponential decay, when increasing message length, of the probability of error of many error-correcting codes. To tackle the long standing problem of computing them exactly, we introduce a general,…
It has been known for a long time that the mutual information between the input sequence and output of a binary symmetric channel (BSC) is upper bounded by the mutual information between the same input sequence and the output of a binary…
Here, we consider the open issue of how the energy efficiency of neural information transmission process in a general neuronal array constrains the network size, and how well this network size ensures the neural information being…
Identification of latent binary sequences from a pool of noisy observations has a wide range of applications in both statistical learning and population genetics. Each observed sequence is the result of passing one of the latent…
We give new constructions of two classes of algebraic code families which are efficiently list decodable with small output list size from a fraction $1-R-\epsilon$ of adversarial errors where $R$ is the rate of the code, for any desired…
Especially in lossless image coding the obtainable compression ratio strongly depends on the amount of noise included in the data as all noise has to be coded, too. Different approaches exist for lossless image coding. We analyze the…
We consider network coding for a noiseless broadcast channel where each receiver demands a subset of messages available at the transmitter and is equipped with noisy side information in the form an erroneous version of the message symbols…
Entropy comparison inequalities are obtained for the differential entropy $h(X+Y)$ of the sum of two independent random vectors $X,Y$, when one is replaced by a Gaussian. For identically distributed random vectors $X,Y$, these are closely…