Related papers: Information Sets of Multiplicity Codes
Colors are used as effective tools of representing and transferring information. Number of colors in a palette is the direct arbiter of the information conveying capacity. Yet it should be well elaborated, since increasing the entropy by…
The security of code-based cryptography relies primarily on the hardness of generic decoding with linear codes. The best generic decoding algorithms are all improvements of an old algorithm due to Prange: they are known under the name of…
Users often have to integrate information about entities from multiple data sources. This task is challenging as each data source may represent information about the same entity in a distinct form, e.g., each data source may use a different…
The theory of computational complexity is used to underpin a recent model of neocortical sensory processing. We argue that encoding into reconstruction networks is appealing for communicating agents using Hebbian learning and working on…
The Moufang loop named for Richard Parker is a central extension of the extended binary Golay code. It the prototypical example of a general class of nonassociative structures known today as code loops, which have been studied from a number…
We examine sets of codes such that certain properties are invariant under the choice of oracle from a range of possible oracles and establish a connection between such codes and Medvedev reductions. In examing the complexity of such sets of…
In this work, we present hardware and software implementations of flexible polar systematic encoders and decoders. The proposed implementations operate on polar codes of any length less than a maximum and of any rate. We describe the…
We consider the decoding of LDPC codes over GF(q) with the low-complexity majority algorithm from [1]. A modification of this algorithm with multiple thresholds is suggested. A lower estimate on the decoding radius realized by the new…
Polar codes are one of the most recent advancements in coding theory and they have attracted significant interest. While they are provably capacity achieving over various channels, they have seen limited practical applications.…
We show that the mutual information, in the sense of Kolmogorov complexity, of any pair of strings $x$ and $y$ is equal, up to logarithmic precision, to the length of the longest shared secret key that two parties, one having $x$ and the…
A generalization of the polar coding scheme called mixed-kernels is introduced. This generalization exploits several homogeneous kernels over alphabets of different sizes. An asymptotic analysis of the proposed scheme shows that its…
This paper proposed the application of post-encryption-compression (PEC) to strengthen the secrecy in the case of distributed encryption where the encryption keys are correlated to each other. We derive the universal code construction for…
Distributions on integers are ubiquitous in probabilistic modeling but remain challenging for many of today's probabilistic programming languages (PPLs). The core challenge comes from discrete structure: many of today's PPL inference…
We use Hidden Markov Models to motivate a quantitative compositional semantics for noninterference-based security with iteration, including a refinement- or "implements" relation that compares two programs with respect to their information…
I construct a secure multi-party scheme to compute a classical function by a succinct use of a specially designed fault-tolerant random polynomial quantum error correction code. This scheme is secure provided that (asymptotically) strictly…
Decoding sequences that stem from multiple transmissions of a codeword over an insertion, deletion, and substitution channel is a critical component of efficient deoxyribonucleic acid (DNA) data storage systems. In this paper, we consider a…
Recently, a new class of error-control codes, the polar codes, have attracted much attention. The polar codes are the first known class of capacity-achieving codes for many important communication channels. In addition, polar codes have…
We study holographic entropy inequalities and their structural properties by making use of a judicious grouping of terms into certain multipartite information quantities. This allows us to recast cumbersome entropic expressions into much…
We propose an entropy function for simplicial complices. Its value gives the expected cost of the optimal encoding of sequences of vertices of the complex, when any two vertices belonging to the same simplex are indistinguishable. We show…
Polar codes were introduced in 2009 by Arikan as the first efficient encoding and decoding scheme that is capacity achieving for symmetric binary-input memoryless channels. Recently, this code family was extended by replacing the…