Iterated Space-Time Code Constructions From Cyclic Algebras

Space-Time Block Codes from Cyclic Division Algebras: An Introduction

Coding theory addresses the problem of transmitting information accurately across noisy channels. When a sender transmits a signal s, it will suffer some changes before it reaches the receiver. The receiver then faces the problem of recovering the intended signal, given that he actually received some altered signal r. The challenge of coding theory, then, is to design a system which not only gi...

Algebras from Standard Constructions

Quotients of orders in cyclic algebras and space-time codes

Let F be a number field with ring of integers OF and D a division F -algebra with a maximal cyclic subfield K. We study rings occurring as quotients of a natural OF -order Λ in D by two-sided ideals. We reduce the problem to studying the ideal structure of Λ/qΛ, where q is a prime ideal in OF , s ≥ 1. We study the case where q remains unramified in K, both when s = 1 and s > 1. This work is mot...

Cyclic Division Algebras: A Tool for Space-Time Coding

Multiple antennas at both the transmitter and receiver ends of a wireless digital transmission channel may increase both data rate and reliability. Reliable high rate transmission over such channels can only be achieved through Space–Time coding. Rank and determinant code design criteria have been proposed to enhance diversity and coding gain. The special case of full-diversity criterion requir...

Constructions Across Time and Space: Perspective Constructions

The German standard language and some of its dialects distinguish two types of directional adverbs, depending on the perspective taken in the speech event. For example, both SHG hinauf vs. herauf mean up. However, the two adverbs differ in that a motion verb modified by SHG hinauf will be construed not only as being UP(WARDS) but also as being AWAYFROM-(the)-ORIGO (we use the term origo to refe...