Random codes based on quasigroups (RCBQ) are cryptcodes, i.e. they are error-correcting codes, which provide information security. Cut-Decoding and 4-Sets-Cut-Decoding algorithms for these codes are defined elsewhere. Also, the performance of these codes f ...
Consider a binary linear code of length N, minimum distance d(min), transmission over the binary erasure channel with parameter 0 < epsilon < 1 or the binary symmetric channel with parameter 0 < epsilon < 1/2, and block-MAP decoding. It was shown by Tillic ...
In the problem of private information retrieval with side information, a single user wants to recover one of the K independent messages which are stored at one or multiple servers. The user initially has a subset of messages as side information. The goal o ...
Polar codes are widely considered as one of the most exciting recent discoveries in channel coding. For short to moderate block lengths, their error-correction performance under list decoding can outperform that of other modern error-correcting codes. Howe ...
We prove polarization theorems for arbitrary classical-quantum (cq) channels. The input alphabet is endowed with an arbitrary Abelian group operation, and an Anion-style transformation is applied using this operation. It is shown that as the number of pola ...
Shannon, in his landmark 1948 paper, developed a framework for characterizing the fundamental limits of information transmission. Among other results, he showed that reliable communication over a channel is possible at any rate below its capacity. In 2008, ...
In this paper, we show that the Hadamard matrix acts as an extractor over the reals of the Renyi Information Dimension (RID), in an analogous way to how it acts as an extractor of the discrete entropy over finite fields. More precisely, we prove that the R ...
The prototypical signal processing pipeline can be divided into four blocks. Representation of the signal in a basis suitable for processing. Enhancement of the meaningful part of the signal and noise reduction. Estimation of important statistical properti ...
Non-malleable codes (NMCs) protect sensitive data against degrees of corruption that prohibit error detection, ensuring instead that a corrupted codeword decodes correctly or to something that bears little relation to the original message. The split-state ...
Non-malleable codes are a generalization of classical error-correcting codes where the act of "corrupting" a codeword is replaced by a "tampering" adversary. Non-malleable codes guarantee that the message contained in the tampered codeword is either the or ...
An alternative type of vector signaling codes having increased pin-efficiency normal vector signaling codes is described. Receivers for these Permutation Modulation codes of Type II use comparators requiring at most one fixed reference voltage. The resulti ...
