Related papers: The theoretical capacity of the Parity Source Code…
Low Rank Parity Check (LRPC) codes form a class of rank-metric error-correcting codes that was purposely introduced to design public-key encryption schemes. An LRPC code is defined from a parity check matrix whose entries belong to a…
Recently, a secrecy measure based on list-reconstruction has been proposed [2], in which a wiretapper is allowed to produce a list of $2^{mR_{L}}$ reconstruction sequences and the secrecy is measured by the minimum distortion over the…
Shannon separation theorem lays the foundation for traditional image compression and transmission schemes, which consist of JPEG type image compression methods and the usual channel coding schemes such as Turbo and LDPC codes. One of the…
"Bounds on information combining" are entropic inequalities that determine how the information (entropy) of a set of random variables can change when these are combined in certain prescribed ways. Such bounds play an important role in…
We describe a slightly sub-exponential time algorithm for learning parity functions in the presence of random classification noise. This results in a polynomial-time algorithm for the case of parity functions that depend on only the first…
We employ the methods of statistical physics to study the performance of Gallager type error-correcting codes. In this approach, the transmitted codeword comprises Boolean sums of the original message bits selected by two…
With the advent of massive data outputs at a regular rate, admittedly, signal processing technology plays an increasingly key role. Nowadays, signals are not merely restricted to physical sources, they have been extended to digital sources…
For the additive Gaussian noise channel with average codeword power constraint, sparse superposition codes and adaptive successive decoding is developed. Codewords are linear combinations of subsets of vectors, with the message indexed by…
Feedback control actively dissipates uncertainty from a dynamical system by means of actuation. We develop a notion of "control capacity" that gives a fundamental limit (in bits) on the rate at which a controller can dissipate the…
We study and compare the Shannon capacity region and the stable throughput region for a random access system in which source nodes multicast their messages to multiple destination nodes. Under an erasure channel model which accounts for…
Shannon's secrecy system is studied in a setting, where both the legitimate decoder and the wiretapper have access to side information sequences correlated to the source, but the wiretapper receives both the coded information and the side…
Quantum error-correcting codes are analyzed from an information-theoretic perspective centered on quantum conditional and mutual entropies. This approach parallels the description of classical error correction in Shannon theory, while…
We recently showed in [1] the superiority of certain structured coding matrices ensembles (such as partial row-orthogonal) for sparse superposition codes when compared with purely random matrices with i.i.d. entries, both…
Inspired by mobile satellite communication systems and the important and prevalent applications of computational tasks, we consider a distributed source coding model for compressing vector-linear functions, which consists of multiple…
This paper presents new lower and upper bounds for the optimal compression of binary prefix codes in terms of the most probable input symbol, where compression efficiency is determined by the nonlinear codeword length objective of…
This article serves as a brief introduction to the Shannon information theory. Concepts of information, Shannon entropy and channel capacity are mainly covered. All these concepts are developed in a totally combinatorial flavor. Some issues…
We show that iterative coding systems can not surpass capacity using only quantities which naturally appear in density evolution. Although the result in itself is trivial, the method which we apply shows that in order to achieve capacity…
Constraints make hard optimization problems even harder to solve on quantum devices because they are implemented with large energy penalties and additional qubit overhead. The parity mapping, which has been introduced as an alternative to…
We consider the problem of transmitting classical and quantum information reliably over an entanglement-assisted quantum channel. Our main result is a capacity theorem that gives a three-dimensional achievable rate region. Points in the…
We study a Pareto-type notion of finite-block optimality for injective source codes, where two codes are compared through the full sequence of expected block lengths. As a concrete and fully analyzable test case, we revisit the four-symbol…