Related papers: Asymptotic fingerprinting capacity for non-binary …
Consider a point-to-point communication system in which the transmitter holds a binary message of length $m$ and transmits a corresponding codeword of length $n$. The receiver's goal is to recover a Boolean function of that message, where…
We present a method to detect lower bounds to the classical capacity of quantum communication channels by means of few local measurements (i.e. without complete process tomography), reconstruction of sets of conditional probabilities, and…
The essential interactive capacity of a discrete memoryless channel is defined in this paper as the maximal rate at which the transcript of any interactive protocol can be reliably simulated over the channel, using a deterministic coding…
The set of all $ q $-ary strings that do not contain repeated substrings of length $ \leqslant\! 3 $ (i.e., that do not contain substrings of the form $ a a $, $ a b a b $, and $ a b c a b c $) constitutes a code correcting an arbitrary…
We firstly extend the interpretation of feedback communication over stationary finite dimensional Gaussian channels as feedback control systems by showing that, the problem of finding stabilizing feedback controllers with maximal reliable…
Channels with synchronization errors, exhibiting deletion and insertion errors, find practical applications in DNA storage, data reconstruction, and various other domains. Presence of insertions and deletions render the channel with memory,…
Finding analytically the statistics of the longest common subsequence (LCS) of a pair of random sequences drawn from c alphabets is a challenging problem in computational evolutionary biology. We present exact asymptotic results for the…
We prove a lower estimate on the increase in entropy when two copies of a conditional random variable $X | Y$, with $X$ supported on $\mathbb{Z}_q=\{0,1,\dots,q-1\}$ for prime $q$, are summed modulo $q$. Specifically, given two i.i.d copies…
For the discrete-time additive white generalized Gaussian noise channel with a generalized input power constraint, with the respective shape and power parameters >= 1, we derive an upper bound on the optimal block error exponent. Explicit…
We analyze the asymptotic performance of nonbinary spatially-coupled low-density parity-check (SC-LDPC) codes built on the general linear group, when the transmission takes place over the binary erasure channel. We propose an efficient…
The Shannon capacity of graphs, introduced by Shannon in 1956 to model zero-error communication, asks for determining the rate of growth of independent sets in strong powers of graphs. Much is still unknown about this parameter, for…
In this paper, we consider single- and multi-user Gaussian channels with feedback under expected power constraints and with non-vanishing error probabilities. In the first of two contributions, we study asymptotic expansions for the…
Any interactive protocol between a pair of parties can be reliably simulated in the presence of noise with a multiplicative overhead on the number of rounds (Schulman 1996). The reciprocal of the best (least) overhead is called the…
Dense coding is arguably the protocol that launched the field of quantum communication. Today, however, more than a decade after its initial experimental realization, the channel capacity remains fundamentally limited as conceived for…
The zero-error capacity of a classical channel is a parameter of its confusability graph, and is equal to the minimum of the values of graph parameters that are additive under the disjoint union, multiplicative under the strong product,…
We derive a single-letter upper bound to the mismatched-decoding capacity for discrete memoryless channels. The bound is expressed as the mutual information of a transformation of the channel, such that a maximum-likelihood decoding error…
If C is a binary linear code, let C^2 be the linear code spanned by intersections of pairs of codewords of C. We construct an asymptotically good family of binary linear codes such that, for C ranging in this family, the C^2 also form an…
We consider the additive white Gaussian noise channels. We prove that the error probability of decoding tends to one exponentially for rates above the capacity and derive the optimal exponent function. We shall demonstrate that the…
In this paper, we present two new constructions of complex codebooks with multiplicative characters, additive characters and trace functions over finite fields, and determine the maximal cross-correlation amplitude of these codebooks. We…
We prove that, for the binary erasure channel (BEC), the polar-coding paradigm gives rise to codes that not only approach the Shannon limit but do so under the best possible scaling of their block length as a~function of the gap to…