Related papers: On the Analysis of Weighted Nonbinary Repeat Multi…
This paper introduces a new combinatorial framework for modeling the growth of binary trees through a discrete evolution process that incorporates a growing rule and an extinction rule. Building upon the theory of increasingly labeled…
In this paper, an expression for the asymptotic growth rate of the number of small linear-weight codewords of irregular doubly-generalized LDPC (D-GLDPC) codes is derived. The expression is compact and generalizes existing results for LDPC…
A ternary message passing (TMP) decoding algorithm for low-density parity-check codes is developed. All messages exchanged between variable and check nodes have a ternary alphabet, and the variable nodes exploit soft information from the…
We consider the problem of neural association for a network of non-binary neurons. Here, the task is to first memorize a set of patterns using a network of neurons whose states assume values from a finite number of integer levels. Later,…
We prove that for every integer $n > 0$ and for every alphabet $\Sigma_k$ of size $k \geq 3$, there exists a necklace of length $n$ whose Burrows-Wheeler Transform (BWT) is completely unclustered, i.e., it consists of exactly $n$ runs with…
This paper is focused on the performance analysis of binary linear block codes (or ensembles) whose transmission takes place over independent and memoryless parallel channels. New upper bounds on the maximum-likelihood (ML) decoding error…
This paper concerns non-overlapping codes, block codes motivated by synchronisation and DNA-based storage applications. Most existing constructions of these codes do not account for the restrictions posed by the physical properties of…
Let $n$ be a prime power, $r$ be a prime with $r\mid n-1$, and $\varepsilon\in (0,1/2)$. Using the theory of multiplicative character sums and superelliptic curves, we construct new codes over $\mathbb F_r$ having length $n$, relative…
We give a new framework based on graph regularity lemmas, for list decoding and list recovery of codes based on spectral expanders. Using existing algorithms for computing regularity decompositions of sparse graphs in (randomized)…
Neural Normalized MinSum (N-NMS) decoding delivers better frame error rate (FER) performance on linear block codes than conventional normalized MinSum (NMS) by assigning dynamic multiplicative weights to each check-to-variable message in…
Weighted sum-rate (WSR) maximization plays a critical role in communication system design. This paper examines three optimization methods for WSR maximization, which ensure convergence to stationary points: two block coordinate ascent (BCA)…
We investigate random spatially coupled low-density parity-check (SC-LDPC) code ensembles over finite fields. Under different variable-node edge-spreading rules, the random Tanner graphs of several coupled ensembles are defined by multiple…
Applying the max-product (and belief-propagation) algorithms to loopy graphs is now quite popular for best assignment problems. This is largely due to their low computational complexity and impressive performance in practice. Still, there…
Reed-Muller (RM) codes are among the oldest, simplest and perhaps most ubiquitous family of codes. They are used in many areas of coding theory in both electrical engineering and computer science. Yet, many of their important properties are…
Linear codes with a few weights have important applications in authentication codes, secret sharing, consumer electronics, etc.. The determination of the parameters such as Hamming weight distributions and complete weight enumerators of…
Most multi-dimensional (more than two dimensions) lattice partitions only form additive quotient groups and lack multiplication operations. This prevents us from constructing lattice codes based on multi-dimensional lattice partitions…
The important problem of weighted sum rate maximization (WSRM) in a multicellular environment is intrinsically sensitive to channel estimation errors. In this paper, we study ways to maximize the weighted sum rate in a linearly precoded…
Irreducible cyclic codes are one of the largest known classes of block codes which have been investigated for a long time. However, their weight distributions are known only for a few cases. In this paper, a class of irreducible cyclic…
Linear complementary dual (LCD) codes are linear codes that intersect with their dual codes trivially. We study the largest minimum weight $d_2(n,k)$ among all binary LCD $[n,k]$ codes and the largest minimum weight $d_3(n,k)$ among all…
Convolutional Neural Networks (CNNs) are one of the most successful deep machine learning technologies for processing image, voice and video data. CNNs require large amounts of processing capacity and memory, which can exceed the resources…