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Design criteria and full-diversity Distributed Space Time Codes (DSTCs) for the two phase transmission based cooperative diversity protocol of Jing-Hassibi and the Generalized Nonorthogonal Amplify and Forward (GNAF) protocol are reported,…
It is well known that the Space-time Block Codes (STBCs) from Complex orthogonal designs (CODs) are single-symbol decodable/symbol-by-symbol decodable (SSD). The weight matrices of the square CODs are all unitary and obtainable from the…
Distributed Orthogonal Space-Time Block Codes (DOSTBCs) achieving full diversity order and single-symbol ML decodability have been introduced recently for cooperative networks and an upper-bound on the maximal rate of such codes along with…
Let K be an algebraic number field of degree d and discriminant D over Q. Let A be an associative algebra over K given by structure constants such that A is isomorphic to the algebra M_n(K) of n by n matrices over K for some positive…
In this paper we propose constellations with suitable structure which allow one to construct codes with excellent diversity using geometrical symmetry and numerical methods. We also demonstrate how these structured constellations…
The topic of this thesis is the development of a versatile and geometrically motivated differential calculus on non-commutative or quantum spaces, providing powerful but easy-to-use mathematical tools for applications in physics and related…
Let $S$ be a unital associative ring and $S[t;\sigma,\delta]$ be a skew polynomial ring, where $\sigma$ is an injective endomorphism of $S$ and $\delta$ a left $\sigma$-derivation. For each $f\in S[t;\sigma,\delta]$ of degree $m>1$ with a…
Starting from the classical r-matrix of the non-standard (or Jordanian) quantum deformation of the sl(2,R) algebra, new triangular quantum deformations for the real Lie algebras so(2,2), so(3,1) and iso(2,1) are simultaneously constructed…
Linear codes are widely studied due to their applications in communication, cryptography, quantum codes, distributed storage and many other fields. In this paper, we use the trace and norm functions over finite fields to construct a family…
The use of Space-Time Block Codes (STBCs) increases significantly the optimal detection complexity at the receiver unless the low-complexity decodability property is taken into consideration in the STBC design. In this paper we propose a…
In this paper, we examine a time-dependent family of two-dimensional algebras. We investigate the conditions under which any two algebras from this family, formed at different times, are isomorphic. Our findings reveal that the flow…
Space-time block codes (STBCs) from non-square complex orthogonal designs are bandwidth efficient when compared with those from square real/complex orthogonal designs. Though there exists rate-1 ROD for any number of transmit antennas,…
In this article we study in detail the category of noncommutative motives of separable algebras Sep(k) over a base field k. We start by constructing four different models of the full subcategory of commutative separable algebras CSep(k).…
In this paper, we construct an infinite family of three-weight binary codes from linear codes over the ring $R=\mathbb{F}_2+v\mathbb{F}_2+v^2\mathbb{F}_2$, where $v^3=1.$ These codes are defined as trace codes. They have the algebraic…
Linear space-time block codes (STBCs) of unitary rate and full diversity, systematically constructed over arbitrary constellations for any number of transmit antennas are introduced. The codes are obtained by generalizing the existing ABBA…
This paper is devoted to the classification and studying properties of complex unital $3$-dimensional structurable algebras. We provide a complete list of non-isomorphic classes, identifying five algebras for type $(2, 1)$ and two algebras…
Perfect space-time codes were first introduced by Oggier et. al. to be the space-time codes that have full rate, full diversity-gain, non-vanishing determinant for increasing spectral efficiency, uniform average transmitted energy per…
We describe a new class of list decodable codes based on Galois extensions of function fields and present a list decoding algorithm. These codes are obtained as a result of folding the set of rational places of a function field using…
We design a polynomial time decoding algorithm for linearized Algebraic Geometry codes with unramified evaluation places, a family of sum-rank metric evaluation codes on division algebras over function fields. By establishing a Serre…
The differential encoding/decoding setup introduced by Kiran et al, Oggier et al and Jing et al for wireless relay networks that use codebooks consisting of unitary matrices is extended to allow codebooks consisting of scaled unitary…