A class of iterated fast decodable space-time codes for 2ⁿ Tx antennas

Abstract

We present an iterative construction of algebraic space-time codes. Starting from a division algebra D, we show how to embed it into a larger ring A = A(D) and give conditions for A to be a new division algebra. Starting from a quaternion division algebra D1, we thus obtain a sequence D1 ⊂ D2 ⊂ . . . of division algebras where Di = A(Di−1). Each of the Di can be used as an underlying structure to build a space-time Ci. Furthermore, the iteration step is done such that fast-decodability of the original code is preserved. We illustrate our technique by creating an iterative version of the Silver code.

Iterated Space-Time Code Constructions From Cyclic Algebras

“…Remark 4: In fact, this construction can be made more general in two ways: (1) one could start with a noncyclic central simple algebra (this has been proposed in [16]), and (2) the map α θ could be applied iteratively to obtain a family of codes for 2 i transmit antennas, i > 0. [17].…”