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A capacity-achieving scheme based on polar codes is proposed for reliable communication over multi-channels which can be directly applied to bit-interleaved coded modulation schemes. We start by reviewing the ground-breaking work of polar…
This paper describes a recursive estimation procedure for multivariate binary densities (probability distributions of vectors of Bernoulli random variables) using orthogonal expansions. For $d$ covariates, there are $2^d$ basis coefficients…
We apply Schrijver's semidefinite programming method to obtain improved upper bounds on generalized distances and list decoding radii of binary codes.
We propose two types of universal codes that are suited to two asymptotic regimes when the output alphabet is possibly continuous. The first class has the property that the error probability decays exponentially fast and we identify an…
Conventional sampling focuses on encoding and decoding bandlimited signals by recording signal amplitudes at known time points. Alternately, sampling can be approached using biologically-inspired schemes. Among these are integrate-and-fire…
We consider the problem of successive-refinement coding for lossy compression of individual sequences, namely, compression in two stages, where in the first stage, a coarse description at a relatively low rate is sent from the encoder to…
We provide a practical implementation of the rubber method of Ahlswede et al. for binary alphabets. The idea is to create the "skeleton" sequence therein via an arithmetic decoder designed for a particular $k$-th order Markov chain. For the…
We introduce a binary embedding framework, called Proximity Preserving Code (PPC), which learns similarity and dissimilarity between data points to create a compact and affinity-preserving binary code. This code can be used to apply fast…
This work develops a rate-distortion-based approach to stochastic Chase decoding of algebraic codes over binary memoryless symmetric (BMS) channels, replacing the heuristics traditionally used to determine flip probabilities with…
We describe the combinatorics that arise in summing a double recursion formula for the enumeration of connected Feynman graphs in quantum field theory. In one index the problem is more tractable and yields concise formulas which are…
Classification of different forms of quantum entanglement is an active area of research, central to development of effective quantum computers, and similar to classification of error-correction codes, where code duality is broadened to…
We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…
A key idea in coding for the broadcast channel (BC) is binning, in which the transmitter encode information by selecting a codeword from an appropriate bin (the messages are thus the bin indexes). This selection is normally done by solving…
This study involves definitions for multiple-counting regular and summation sequences of rho. My paper introduces and proves recurrent relationships for multiple-counting sequences and shows their association with Fermat's little theorem. I…
A key problem in constrained random verification (CRV) concerns generation of input stimuli that result in good coverage of the system's runs in targeted corners of its behavior space. Existing CRV solutions however provide no formal…
An alternative permutation decoding method is described which can be used for any binary systematic encoding scheme, regardless whether the code is linear or not. Thus, the method can be applied to some important codes such as Z2Z4-linear…
The goal of this work is to segment the objects in an image that are referred to by a sequence of linguistic descriptions (referring expressions). We propose a deep neural network with recurrent layers that output a sequence of binary…
The problem of low complexity, close to optimal, channel decoding of linear codes with short to moderate block length is considered. It is shown that deep learning methods can be used to improve a standard belief propagation decoder,…
The paper suggests a method of optimal extension of one-sided semi-infinite sequences of a general type by traces of band-limited sequences in deterministic setting, i.e. without probabilistic assumptions. The method requires to solve a…
Truncated sum rules have been used to calculate the fundamental limits of the nonlinear susceptibilities; and, the results have been consistent with all measured molecules. However, given that finite-state models result in inconsistencies…