Related papers: Generalized Random Gilbert-Varshamov Codes: Typica…
Error probabilities of random codes for memoryless channels are considered in this paper. In the area of communication systems, admissible error probability is very small and it is sometimes more important to discuss the relative gap…
Braided convolutional codes (BCCs) are a class of spatially coupled turbo-like codes that can be described by a $(2,3)$-regular compact graph. In this paper, we introduce a family of $(d_v,d_c)$-regular GLDPC codes with convolutional code…
Bounds on the reliability function for the discrete memoryless relay channel are derived using the method of types. Two achievable error exponents are derived based on partial decode-forward and compress-forward which are well-known…
The bias-variance decomposition is a central result in statistics and machine learning, but is typically presented only for the squared error. We present a generalization of the bias-variance decomposition where the prediction error is a…
This paper studies the generalization performance of iterates obtained by Gradient Descent (GD), Stochastic Gradient Descent (SGD) and their proximal variants in high-dimensional robust regression problems. The number of features is…
In the problem of variable-length $\delta$-channel resolvability, the channel output is approximated by encoding a variable-length uniform random number under the constraint that the variational distance between the target and approximated…
We study the minimum distance of codes defined on bipartite graphs. Weight spectrum and the minimum distance of a random ensemble of such codes are computed. It is shown that if the vertex codes have minimum distance $\ge 3$, the overall…
The Good-Turing (GT) estimator for the missing mass (i.e., total probability of missing symbols) in $n$ samples is the number of symbols that appeared exactly once divided by $n$. For i.i.d. samples, the bias and squared-error risk of the…
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,…
Except for a few simple digital modulation techniques, derivation of average bit error probability over fading channels is difficult and is an involved process. In this letter, curve fitting technique has been employed to express bit error…
This paper proposes a novel approach to the statistical characterization of non-central complex Gaussian quadratic forms (CGQFs). Its key strategy is the generation of an auxiliary random variable (RV) that converges in distribution to the…
How well can we approximate a quantum channel output state using a random codebook with a certain size? In this work, we study the quantum soft covering problem. Namely, we use a random codebook with codewords independently sampled from a…
The error performance of the ensemble of typical LDPC codes transmitted over the binary erasure channel (BEC) is analyzed. In the past, lower bounds on the error exponents were derived. In this paper a probabilistic upper bound on this…
We propose a source/channel duality in the exponential regime, where success/failure in source coding parallels error/correctness in channel coding, and a distortion constraint becomes a log-likelihood ratio (LLR) threshold. We establish…
In this paper, we provide three applications for $f$-divergences: (i) we introduce Sanov's upper bound on the tail probability of the sum of independent random variables based on super-modular $f$-divergence and show that our generalized…
The fundamental limits of channels with mismatched decoding are addressed. A general formula is established for the mismatch capacity of a general channel, defined as a sequence of conditional distributions with a general decoding metrics…
This paper considers the problem of variable-length lossy source coding. The performance criteria are the excess distortion probability and the cumulant generating function of codeword lengths. We derive a non-asymptotic fundamental limit…
We consider a family of variational time discretizations that are generalizations of discontinuous Galerkin (dG) and continuous Galerkin-Petrov (cGP) methods. The family is characterized by two parameters. One describes the polynomial…
The aim of this paper is to give a precise asymptotic description of some eigenvalue statistics stemming from random matrix theory. More precisely, we consider random determinants of the GUE, Laguerre, Uniform Gram and Jacobi beta ensembles…
We establish a general formula for the maximum size of finite length block codes with minimum pairwise distance no less than $d$. The achievability argument involves an iterative construction of a set of radius-$d$ balls, each centered at a…