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

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 D_i = A(D_i-1). Each of the D_i can be used as an underlying structure to build a space-time C_i. 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.