Related papers: Error-Correcting Codes That Nearly Saturate Shanno…
This paper investigates the maximal channel coding rate achievable at a given blocklength $n$ and error probability $\epsilon$, when the codewords are subject to a long-term (i.e., averaged-over-all-codeword) power constraint. The…
This paper considers coding for so-called partially stuck (defect) memory cells. Such memory cells can only store partial information as some of their levels cannot be used fully due to, e.g., wearout. First, we present new constructions…
Entanglement renormalization can be viewed as an encoding circuit for a family of approximate quantum error correcting codes. The logical information becomes progressively more well-protected against erasure errors at larger length scales.…
The capacity of line networks with buffer size constraints is an open, but practically important problem. In this paper, the upper bound on the achievable rate of a class of codes, called batched codes, is studied for line networks. Batched…
We show that entirely quantum Shannon theoretic methods, based on von Neumann entropies and their properties, can be used to derive Singleton bounds on the performance of entanglement-assisted hybrid classical-quantum (EACQ) error…
We construct error correcting codes for jointly transmitting a finite set of independent messages to an 'informed receiver' which has prior knowledge of the values of some subset of the messages as side information. The transmitter is…
Although for a number of semilinear stochastic wave equations existence and uniqueness results for corresponding solution processes are known from the literature, these solution processes are typically not explicitly known and numerical…
We investigate the relation between the girth and the guaranteed error correction capability of $\gamma$-left regular LDPC codes when decoded using the bit flipping (serial and parallel) algorithms. A lower bound on the number of variable…
We compute Shannon capacity of nonlinear channels with regenerative elements. Conditions are found under which capacity of such nonlinear channels is higher than the Shannon capacity of the classical linear additive white Gaussian noise…
The purpose of this study is to construct a near capacity Irregular Turbo Code and to evaluate its performance over Gaussian channel. The methodology used to evaluate and measure the performance of the new design is by simulating the system…
Covariant codes are quantum codes such that a symmetry transformation on the logical system could be realized by a symmetry transformation on the physical system, usually with limited capability of performing quantum error correction (an…
This paper explores the possibilities and limitations of error correction by the structural simplicity of error mechanisms. Specifically, we consider channel models, called \emph{samplable additive channels}, in which (a) errors are…
Tuning a complex simulation code refers to the process of improving the agreement of a code calculation with respect to a set of experimental data by adjusting parameters implemented in the code. This process belongs to the class of inverse…
In this paper q-ary Raptor codes under ML decoding are considered. An upper bound on the probability of decoding failure is derived using the weight enumerator of the outer code, or its expected weight enumerator if the outer code is drawn…
Spinal codes are a type of capacity-achieving rateless codes that have been proved to approach the Shannon capacity over the additive white Gaussian noise (AWGN) channel and the binary symmetric channel (BSC). In this paper, we aim to…
The lower bound on the decoding error probability for the optimal code given a signal-to-noise ratio and a code rate are investigated in this letter for the reconfigurable intelligent surface (RIS) communication system over a Rician fading…
We derive the coding capacity for duplication-correcting codes capable of correcting any number of duplications. We do so both for reverse-complement duplications, as well as palindromic (reverse) duplications. We show that except for…
We provide a systematic way of constructing entanglement-assisted quantum error-correcting codes via graph states in the scenario of preexisting perfectly protected qubits. It turns out that the preexisting entanglement can help beat the…
This paper considers delay-limited communication over quasi-static fading channels under a long-term power constraint. A sequence of length-$n$ delay-limited codes for a quasi-static fading channel is said to be capacity-achieving if the…
The theory of error-correcting codes is concerned with constructing codes that optimize simultaneously transmission rate and relative minimum distance. These conflicting requirements determine an asymptotic bound, which is a continuous…