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In this paper, the linear programming (LP) decoder for binary linear codes, introduced by Feldman, et al. is extended to joint-decoding of binary-input finite-state channels. In particular, we provide a rigorous definition of LP…
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…
Minimal codes are linear codes where all non-zero codewords are minimal, i.e., whose support is not properly contained in the support of another codeword. The minimum possible length of such a $k$-dimensional linear code over $\mathbb{F}_q$…
Efficient decoding is crucial to high-throughput and power-sensitive wireless communication scenarios. A theoretical analysis of the performance-complexity tradeoff toward low-complexity decoding is required for a better understanding of…
In this work we explore possibilities for coding when information worlds have different (semantic) values. We introduce a loss function that expresses the overall performance of a coding scheme for discrete channels and exchange the usual…
The purpose of this paper is to present the structure of the linear codes over a finite field with q elements that have a permutation automorphism of order m. These codes can be considered as generalized quasi-cyclic codes. Quasi-cyclic…
Minimal codewords have applications in decoding linear codes and in cryptography. We study the maximum number of minimal codewords in binary linear codes of a given length and dimension. Improved lower and upper bounds on the maximum number…
Low-density parity-check codes together with belief propagation (BP) decoding are known to be well-performing for large block lengths. However, for short block lengths there is still a considerable gap between the performance of the BP…
In this paper, we first introduce the extended binary representation of non-binary codes, which corresponds to a covering graph of the bipartite graph associated with the non-binary code. Then we show that non-binary codewords correspond to…
Neural Language Models of Code, or Neural Code Models (NCMs), are rapidly progressing from research prototypes to commercial developer tools. As such, understanding the capabilities and limitations of such models is becoming critical.…
Millions of repetitive code snippets are submitted to code repositories every day. To search from these large codebases using simple natural language queries would allow programmers to ideate, prototype, and develop easier and faster.…
Encodings or the proof of their absence are the main way to compare process calculi. To analyse the quality of encodings and to rule out trivial or meaningless encodings, they are augmented with quality criteria. There exists a bunch of…
Understanding binary code is an essential but complex software engineering task for reverse engineering, malware analysis, and compiler optimization. Unlike source code, binary code has limited semantic information, which makes it…
In this article we consider linear codes coming from skew-symmetric determinantal varieties, which are defined by the vanishing of minors of a certain fixed size in the space of skew-symmetric matrices. In odd characteristic, the minimum…
In his thesis, Wiberg showed the existence of thresholds for families of regular low-density parity-check codes under min-sum algorithm decoding. He also derived analytic bounds on these thresholds. In this paper, we formulate similar…
Black-box probing models can reliably extract linguistic features like tense, number, and syntactic role from pretrained word representations. However, the manner in which these features are encoded in representations remains poorly…
We present the theory of linear rank-metric codes from the point of view of their fundamental parameters. These are: the minimum rank distance, the rank distribution, the maximum rank, the covering radius, and the field size. The focus of…
The equivalence test is a main part in any classification problem. It helps to prove bounds for the main parameters of the considered combinatorial structures and to study their properties. In this paper, we present algorithms for…
Density evolution (DE) is one of the most powerful analytical tools for low-density parity-check (LDPC) codes on memoryless binary-input/symmetric-output channels. The case of non-symmetric channels is tackled either by the LDPC coset code…
We derive bounds on the asymptotic density of parity-check matrices and the achievable rates of binary linear block codes transmitted over memoryless binary-input output-symmetric (MBIOS) channels. The lower bounds on the density of…