相关论文: On the Existence of Universally Decodable Matrices

Decoding quantum error-correcting codes is a key challenge in enabling fault-tolerant quantum computation. In the classical setting, linear programming (LP) decoders offer provable performance guarantees and can leverage fast practical…

We introduce a new analysis technique to derive a single-letter upper bound on the mismatch capacity of a stationary, single-user, memoryless channel with a decoding metric $q$. Our bound is obtained by considering a multicast transmission…

Fast decoding algorithms are decisive for real-time quantum error correction and for analyzing properties of error correction codes. Here, we develop variants of the union-find decoder that simplify its implementation and provide potential…

We consider quantum MDS (QMDS) codes for quantum systems of dimension $q$ with lengths up to $q^2+2$ and minimum distances up to $q+1$. We show how starting from QMDS codes of length $q^2+1$ based on cyclic and constacyclic codes, new QMDS…

Euclidean distance matrices (EDM) are symmetric nonnegative matrices with several interesting properties. In this article, we introduce a wider class of matrices called generalized Euclidean distance matrices (GDMs) that include EDMs. Each…

Although a unique solution is guaranteed in the Linear complementarity problem (LCP) when the matrix $\mathbf{M}$ is positive definite, practical applications often involve cases where $\mathbf{M}$ is only positive semi-definite, leading to…

This paper introduces a new approach to proving that a sequence of deterministic linear codes achieves capacity on an erasure channel under maximum a posteriori decoding. Rather than relying on the precise structure of the codes, this…

In this paper, we introduce a new way of constructing and decoding multipermutation codes. Multipermutations are permutations of a multiset that generally consist of duplicate entries. We first introduce a class of binary matrices called…

Recent investigations suggest that the discrete linear unitary group $U(N)$ can be represented by interlacing a finite sequence of diagonal phase operations with an intervening unitary operator. However, despite rigorous numerical…

We introduce a new approach to proving that a sequence of deterministic linear codes achieves capacity on an erasure channel under maximum a posteriori decoding. Rather than relying on the precise structure of the codes our method exploits…

Let $\mathbb{F}$ be a finite field of odd characteristic. When $|\mathbb{F}|\ge 5$, we prove that every matrix $A$ admits a decomposition into $D+M$ where $D$ is diagonalizable and $M^2=0$. For $\mathbb{F}=\mathbb{F}_3$, we show that such…

We propose two types of universal codes that are suited to two asymptotic regimes when the output alphabet is possibly continuous. The first class has the property that the error probability decays exponentially fast and we identify an…

A universal cycle for permutations is a word of length n! such that each of the n! possible relative orders of n distinct integers occurs as a cyclic interval of the word. We show how to construct such a universal cycle in which only n+1…

We show universally attainable exponents for the decoding error and the mutual information and universally attainable equivocation rates for the conditional entropy for the broadcast channels with confidential messages. The error exponents…

We show how universal codes can be used for solving some of the most important statistical problems for time series. By definition, a universal code (or a universal lossless data compressor) can compress any sequence generated by a…

We consider the problem of designing a low-complexity decoder for antipodal uniquely decodable (UD) /errorless code sets for overloaded synchronous code-division multiple access (CDMA) systems, where the number of signals Kamax is the…

This work contains two main contributions concerning the asymmetric broadcast channel. The first is an analysis of the exact random coding error exponents for both users, and the second is the derivation of universal decoders for both…

This paper proposes the design of polar and convolutional coset codes for the unequal message protection (UMP) in the short blocklength regime, to overcome the rate loss introduced by preamble-based solutions. After providing conditions to…

The $MLS$ conjecture states that every finite simple group has a minimal logarithmic signature. The aim of this paper is proving the existence of a minimal logarithmic signature for some simple unitary groups $PSU_{n}(q)$. We report a gap…

Good quantum error-correcting codes that fulfill practical considerations, such as simple encoding circuits and efficient decoders, are essential for functional quantum information processing systems. Quantum polar codes satisfy some of…