相关论文: More Efficient Algorithms and Analyses for Unequal…

A new class of folded subspace codes for noncoherent network coding is presented. The codes can correct insertions and deletions beyond the unique decoding radius for any code rate $R\in[0,1]$. An efficient interpolation-based decoding…

Quantum error correction is a critical component for scaling up quantum computing. Given a quantum code, an optimal decoder maps the measured code violations to the most likely error that occurred, but its cost scales exponentially with the…

We consider the embedding problem in coding theory: given an independence (a code-related property) and an independent language $L$, find a maximal independent language containing $L$. We consider the case where the code-related property is…

The problem of compression in standard information theory consists of assigning codes as short as possible to numbers. Here we consider the problem of optimal coding -- under an arbitrary coding scheme -- and show that it predicts Zipf's…

In the search with wildcards problem [Ambainis, Montanaro, Quantum Inf.~Comput.'14], one's goal is to learn an unknown bit-string $x \in \{-1,1\}^n$. An algorithm may, at unit cost, test equality of any subset of the hidden string with a…

This paper investigates the size in bits of the LZ77 encoding, which is the most popular and efficient variant of the Lempel-Ziv encodings used in data compression. We prove that, for a wide natural class of variable-length encoders for…

Building an infinite square-free word by appending one letter at a time while simultaneously avoiding the creation of squares is most likely to fail. When the alphabet has two letters this approach is impossible. When the alphabet has three…

We introduce \emph{Term Coding}, a novel framework for analysing extremal problems in discrete mathematics by encoding them as finite systems of \emph{term equations} (and, optionally, \emph{non-equality constraints}). In its basic form,…

String matching is the problem of finding all the occurrences of a pattern in a text. We propose improved versions of the fast family of string matching algorithms based on hashing $q$-grams. The improvement consists of considering minimal…

The rapid advancement of large language models (LLMs) has significantly improved code completion tasks, yet the trade-off between accuracy and computational cost remains a critical challenge. While using larger models and incorporating…

We introduce a new framework term coding for extremal problems in discrete mathematics and information flow, where one chooses interpretations of function symbols so as to maximise the number of satisfying assignments of a finite system of…

In Index coding there is a single sender with multiple messages and multiple receivers each wanting a different set of messages and knowing a different set of messages a priori. The Index Coding problem is to identify the minimum number of…

Motivated by distributed storage applications, we investigate the degree to which capacity achieving encodings can be efficiently updated when a single information bit changes, and the degree to which such encodings can be efficiently…

The rate of convergence of the distribution of the length of the longest increasing subsequence, toward the maximal eigenvalue of certain matrix ensembles, is investigated. For finite-alphabet uniform and nonuniform i.i.d. sources, a rate…

The order of letters is not always relevant in a communication task. This paper discusses the implications of order irrelevance on source coding, presenting results in several major branches of source coding theory: lossless coding,…

We compute the integral of a function or the expectation of a random variable with minimal cost and use, for our new algorithm and for upper bounds of the complexity, i.i.d. samples. Under certain assumptions it is possible to select a…

In this paper we consider an interacting two-agent sequential decision-making problem consisting of a Markov source process, a causal encoder with feedback, and a causal decoder. Motivated by a desire to foster links between control and…

The so-called fast polar decoding schedules are meant to improve the decoding speed of the sequential-natured successive cancellation list decoders. The decoding speedup is achieved by replacing various parts of the serial decoding process…

We present a two-step decoder for the parity code and evaluate its performance in code-capacity and faulty-measurement settings. For noiseless measurements, we find that the decoding problem can be reduced to a series of repetition codes…

An index for a finite automaton is a powerful data structure that supports locating paths labeled with a query pattern, thus solving pattern matching on the underlying regular language. In this paper, we solve the long-standing problem of…