Related papers: Codes over Matrix Rings for Space-Time Coded Modul…
Let $R=\mathbb{Z}_{4}[u]/\langle u^k\rangle=\mathbb{Z}_{4}+u\mathbb{Z}_{4}+\ldots+u^{k-1}\mathbb{Z}_{4}$ ($u^k=0$) where $k\in \mathbb{Z}^{+}$ satisfies $k\geq 2$. For any odd positive integer $n$, it is known that cyclic codes over $R$ of…
This paper considers a new alphabet set, which is a ring that we call $\mathbb{F}_4R$, to construct linear error-control codes. Skew cyclic codes over the ring are then investigated in details. We define a nondegenerate inner product and…
We consider a network coding setting where some of the messages and edges have fixed alphabet sizes, that do not change when we increase the common alphabet size of the rest of the messages and edges. We prove that the problem of deciding…
Additive cyclic codes over Galois rings were investigated in previous works. In this paper, we investigate the same problem but over a more general ring family, finite commutative chain rings. When we focus on non-Galois finite commutative…
In this paper, we shed light on how an adaptive, efficient error coding in the transport layer helps ensure the application requirements. We recap the use of MDS codes and show that binary coding can significantly reduce the complexity and…
Let $p$ be a prime integer, $n,s\geq 2$ be integers satisfying ${\rm gcd}(p,n)=1$, and denote $R=\mathbb{Z}_{p^s}[v]/\langle v^2-pv\rangle$. Then $R$ is a local non-principal ideal ring of $p^{2s}$ elements. First, the structure of any…
Marton's inner bound is the best known achievable region for a general discrete memoryless broadcast channel. To compute Marton's inner bound one has to solve an optimization problem over a set of joint distributions on the input and…
A new inner bound on the capacity region of a general index coding problem is established. Unlike most existing bounds that are based on graph theoretic or algebraic tools, the bound is built on a random coding scheme and optimal decoding,…
Skew polynomial rings over finite fields ([7] and [10]) and over Galois rings ([8]) have been used to study codes. In this paper, we extend this concept to finite chain rings. Properties of skew constacyclic codes generated by monic right…
Ultra-reliable low-latency communication is essential in mission-critical settings, including military applications, where persistent and asymmetric link blockages caused by mobility, jamming, or adversarial attacks can disrupt…
In this paper, a design criterion for space-time block codes (STBC) is proposed for two-user MIMO interference channels when a group zero-forcing (ZF) algorithm is applied at each receiver to eliminate the inter-user interference. Based on…
We consider a downlink 1-bit quantized multiuser (MU) multiple-input-multiple-output (MIMO) system, where 1-bit digital-to-analog (DACs) and analog-to-digital converters (ADCs) are used at the transmitter and the receiver for economical and…
In this work, spatial diversity techniques in the area of multiple-input multiple-output (MIMO) diffusion-based molecular communications (DBMC) are investigated. For transmitter-side spatial coding, Alamouti-type coding and repetition MIMO…
This paper presents encoding and decoding algorithms for several families of optimal rank metric codes whose codes are in restricted forms of symmetric, alternating and Hermitian matrices. First, we show the evaluation encoding is the right…
Motivated by communication channels in which the transmitted sequences are subject to random permutations, as well as by certain DNA storage systems, we study the error control problem in settings where the information is stored/transmitted…
An important class of codes widely used in applications is the class of convolutional codes. Most of the literature of convolutional codes is devoted to con- volutional codes over finite fields. The extension of the concept of convolutional…
We begin this chapter by introducing the simple algebraic structure of cyclic codes over finite fields. This structure undergoes a series of generalizations to present algebraic descriptions of constacyclic, quasi-cyclic (QC), quasi-twisted…
We establish several new results on Marton's coding scheme and its corresponding inner bound on the capacity region of the general broadcast channel. We show that unlike the Gaussian case, Marton's coding scheme without superposition coding…
This paper considers space-time coding over several independently Rayleigh faded blocks. In particular we will concentrate on giving upper bounds for the coding gain of lattice space-time codes as the number of blocks grow. This problem was…
Lately, different methods for broadcasting future digital TV in a single frequency network (SFN) have been under an intensive study. To improve the transmission to also cover suburban and rural areas, a hybrid scheme may be used. In hybrid…