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Conflict-avoiding codes (CACs) have been used in multiple-access collision channel without feedback. The size of a CAC is the number of potential users that can be supported in the system. A code with maximum size is called optimal. The use…

Index coding, or broadcasting with side information, is a network coding problem of most fundamental importance. In this problem, given a directed graph, each vertex represents a user with a need of information, and the neighborhood of each…

A new method of constructing optimum constant weight codes over F_2 based on a generalized $(u, u+v)$ construction is presented. We present a new method of constructing superimposed code $C_{(s_1,s_2,\cdots,s_I)}^{(h_1, h_2, \cdots, h_I)}$…

Traditional error-correcting codes (ECCs) assume a fixed message length, but many scenarios involve ongoing or indefinite transmissions where the message length is not known in advance. For example, when streaming a video, the user should…

We consider the problem of constructing prefix-free codes in which a designated symbol, a space, can only appear at the end of codewords. We provide a linear-time algorithm to construct almost-optimal codes with this property, meaning that…

We generalized to higher dimensions the notions of optical orthogonal codes. We establish uper bounds on the capacity of general $ n $-dimensional OOCs, and on specific types of ideal codes (codes with zero off-peak autocorrelation). The…

In this paper we consider the class of anti-uniform Huffman codes and derive tight lower and upper bounds on the average length, entropy, and redundancy of such codes in terms of the alphabet size of the source. The Fibonacci distributions…

An equi-differece conflict-avoiding code $(CAC^{e})\ \mathcal{C}$ of length $n$ and weight $\omega$ is a collection of $\omega$-subsets (called codewords) which has the form $\{0,i,2i,\cdots,(\omega-1)i\}$ of $\mathbb{Z}_{n}$ such that…

Let $C$ be a binary code of length $n$ with distances $0<d_1<\cdots<d_s\le n$. In this note we prove a general upper bound on the size of $C$ without any restriction on the distances $d_i$. The bound is asymptotically optimal.

We put forth new models for universal channel coding. Unlike standard codes which are designed for a specific type of channel, our most general universal code makes communication resilient on every channel, provided the noise level is below…

We discuss the interest of escort distributions and R\'enyi entropy in the context of source coding. We first recall a source coding theorem by Campbell relating a generalized measure of length to the R\'enyi-Tsallis entropy. We show that…

Collective coherent (CC) errors are inevitable, as every physical qubit undergoes free evolution under its kinetic Hamiltonian. These errors can be more damaging than stochastic Pauli errors because they affect all qubits coherently,…

Optimal encoding of classical data for statistical inference using quantum computing is investigated. A universal encoder is sought that is optimal for a wide array of statistical inference tasks. Accuracy of any statistical inference is…

We prove a variety of new and refined uniform continuity bounds for entropies of both classical random variables on an infinite state space and of quantum states of infinite-dimensional systems. We obtain the first tight continuity estimate…

It is well known that Space-Time Block Codes (STBCs) from orthogonal designs (ODs) are single-symbol decodable/symbol-by-symbol decodable (SSD) and are obtainable from unitary matrix representations of Clifford algebras. However, SSD codes…

Uniform continuity bounds on entropies are generally expressed in terms of a single distance measure between a pair of probability distributions or quantum states, typically, the total variation distance or trace distance. However, if an…

The groupcast index coding problem is the most general version of the classical index coding problem, where any receiver can demand messages that are also demanded by other receivers. Any groupcast index coding problem is described by its…

Recently, Gilmer proved the first constant lower bound for the union-closed sets conjecture via an information-theoretic argument. The heart of the argument is an entropic inequality involving the OR function of two i.i.d.\ binary vectors,…

In a lossless compression system with target lengths, a compressor ${\cal C}$ maps an integer $m$ and a binary string $x$ to an $m$-bit code $p$, and if $m$ is sufficiently large, a decompressor ${\cal D}$ reconstructs $x$ from $p$. We call…

Consider the following framework of universal decoding suggested in [MerhavUniversal]. Given a family of decoding metrics and random coding distribution (prior), a single, universal, decoder is optimal if for any possible channel the…