Related papers: Error-Resilient Weakly Constrained Coding via Row-…
Inspired by prior work by Tian and by Cao and Xu, this paper presents an efficient computer-aided framework to characterize the fundamental limits of coded caching systems under the constraint of linear coding. The proposed framework…
Consider a source and multiple users who observe the independent and identically distributed (i.i.d.) copies of correlated Gaussian random variables. The source wishes to compress its observations and store the result in a public database…
Linear codes with few weights have applications in consumer electronics, communication, data storage system, secret sharing, authentication codes, association schemes, and strongly regular graphs. This paper first generalizes the method of…
We introduce a new class of non-standard variable-length codes, called adaptive codes. This class of codes associates a variable-length codeword to the symbol being encoded depending on the previous symbols in the input data string. An…
Convolutional codes are constructed, designed and analysed using row and/or block structures of unit algebraic schemes. Infinite series of such codes and of codes with specific properties are derived. Properties are shown algebraically and…
Random linear codes (RLCs) are well known to have nice combinatorial properties and near-optimal parameters in many different settings. However, getting explicit constructions matching the parameters of RLCs is challenging, and RLCs are…
Minimal linear codes have significant applications in secret sharing schemes and secure two-party computation. There are several methods to construct linear codes, one of which is based on functions over finite fields. Recently, many…
In 2015, Archdeacon proposed the notion of Heffter arrays in view of its connection to several other combinatorial objects. In the same paper he also presented the following variant. A weak Heffter array $\mathrm{W}\mathrm{H}(m,n;h,k)$ is…
The efficiency of a code is estimated by its redundancy $R$, while the complexity of a code is estimated by its average delay $\bar N$. In this work we construct word-based codes, for which $R \lesssim \bar N^{-5/3}$. Therefore, word-based…
This paper investigates fundamental properties of nonlinear binary codes by looking at the codebook matrix not row-wise (codewords), but column-wise. The family of weak flip codes is presented and shown to contain many beautiful properties.…
Clustering a signed graph means partitioning the vertices into sets ("clusters") so that every positive edge, and no negative edge, is within a cluster. Clustering is not always possible; the obstruction is circles with exactly one negative…
The strong converse for a coding theorem shows that the optimal asymptotic rate possible with vanishing error cannot be improved by allowing a fixed error. Building on a method introduced by Gu and Effros for centralized coding problems, we…
In software, there are the errors anticipated at specification and design time, those encountered at development and testing time, and those that happen in production mode yet never anticipated. In this paper, we aim at reasoning on the…
This paper discusses the problem of weakly supervised classification, in which instances are given weak labels that are produced by some label-corruption process. The goal is to derive conditions under which loss functions for weak-label…
We provide a general formulation for the code-based test compression problem with fixed-length input blocks and propose a solution approach based on Evolutionary Algorithms. In contrast to existing code-based methods, we allow unspecified…
A new method to identify all sufficiently long repeating substrings in one or several symbol sequences is proposed. The method is based on a specific gauge applied to symbol sequences that guarantees identification of the repeating…
Many safety-critical real-time systems operate under harsh environment and are subject to soft errors caused by transient or intermittent faults. It is critical and yet often very challenging to apply fault tolerance techniques in these…
We consider recursive decoding techniques for RM codes, their subcodes, and newly designed codes. For moderate lengths up to 512, we obtain near-optimum decoding with feasible complexity.
In this work, we study two types of constraints on two-dimensional binary arrays. In particular, given $p,\epsilon>0$, we study (i) The $p$-bounded constraint: a binary vector of size $m$ is said to be $p$-bounded if its weight is at most…
Given a noiseless protocol $\pi_0$ computing a function $f(x, y)$ of Alice and Bob's private inputs $x, y$, the goal of interactive coding is to construct an error-resilient protocol $\pi$ computing $f$ such that even if some fraction of…