Related papers: The DMT classification of real and quaternionic la…
The ground spaces of a vector space of hermitian matrices, partially ordered by inclusion, form a lattice constructible from top to bottom in terms of intersections of maximal ground spaces. In this paper we characterize the lattice…
Linear codes play a central role in coding theory and have applications in several branches of mathematics. For error correction purposes the minimum Hamming distance should be as large as possible. Linear codes related to applications in…
The diversity-multiplexing tradeoff (DMT) provides a fundamental performance metric for different multiple-input multiple-output (MIMO) schemes in wireless communications. In this paper, we explore the block fading optical wireless…
A construction of a new family of distributed space time codes (DSTCs) having full diversity and low Maximum Likelihood (ML) decoding complexity is provided for the two phase based cooperative diversity protocols of Jing-Hassibi and the…
This paper investigates the theory of sum-rank metric codes for which the individual matrix blocks may have different sizes. Various bounds on the cardinality of a code are derived, along with their asymptotic extensions. The duality theory…
Let $A_q(n,d)$ be the maximum order (maximum number of codewords) of a $q$-ary code of length $n$ and Hamming distance at least $d$. And let $A(n,d,w)$ that of a binary code of constant weight $w$. Building on results from algebraic graph…
An adaptive distributed space-time coding (DSTC) scheme is proposed for two-hop cooperative MIMO networks. Linear minimum mean square error (MMSE) receive filters and adjustable code matrices are considered subject to a power constraint…
We study the diversity-multiplexing tradeoff (DMT) for the slow fading interference channel with a relay (ICR). We derive four inner bounds on the DMT region: the first is based on the compress-and-forward (CF) relaying scheme, the second…
In the realm of rank-metric codes, Maximum Rank Distance (MRD) codes are optimal algebraic structures attaining the Singleton-like bound. A major open problem in this field is determining whether an MRD code can be extended to a longer one…
This paper considers the optimization of multi-edge type low-density parity-check (METLDPC) codes to maximize the decoding threshold. We propose an algorithm to jointly optimize the node degree distribution and the multi-edge structure of…
One-dimensional quasilattices are classified into mutual local-derivability (MLD) classes on the basis of geometrical and number-theoretical considerations. Most quasilattices are ternary, and there exist an infinite number of MLD classes.…
We consider cooperative relay communication in a fading channel environment under the Orthogonal Amplify and Forward (OAF) and Orthogonal and Non-Orthogonal Selection Decode and Forward (OSDF and NSDF) protocols. For all these protocols, we…
Let $Q$ be an ideal (downward-closed set) in the lattice of linear subspaces of $(\mathbb F_q)^n$, ordered by inclusion. For $0 \le k \le n$, let $\mu_k(Q)$ denote the fraction of $k$-dimensional subspaces that belong to $Q$. We show that…
In this paper we introduce a new right preprocessing method for the decoding of 2x2 algebraic STBCs, called algebraic reduction, which exploits the multiplicative structure of the code. The principle of the new reduction is to absorb part…
We review the main results of the theory of rank-metric codes, with emphasis on their combinatorial properties. We study their duality theory and MacWilliams identities, comparing in particular rank-metric codes in vector and matrix…
We consider $q$-ary (linear and nonlinear) block codes with exactly two distances: $d$ and $d+\delta$. Several combinatorial constructions of optimal such codes are given. In the linear (but not necessary projective) case, we prove that…
Explicit codes are constructed that achieve the diversity-multiplexing gain tradeoff of the cooperative-relay channel under the dynamic decode-and-forward protocol for any network size and for all numbers of transmit and receive antennas at…
We study a space--time block code from a maximal order in the definite quaternion algebra $(-1,-3)_{\Q}$. Its embedding into $\C^{2\times 2}$ yields an Alamouti--Eisenstein code over $\Z[w]$ with full diversity, orthogonality, and…
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…
Multivariate multiplicity codes (Kopparty, Saraf, and Yekhanin, J. ACM 2014) are linear codes where the codewords are described by evaluations of multivariate polynomials (with a degree bound) and their derivatives up to a fixed order, on a…