Fast Decoding of the Golden Code by Diophantine Approximation

The Golden Code is incorporated in the IEEE 802.16 standard and is representative of a large class of space-time codes where performance is determined by the difficulty of solving an associated Diophantine approximation problem. This paper develops a new approach to coherent decoding where channel state information is used to select from a plurality of zero-forcing decoders. The selection is made to maximize effective signal to noise ratio and the underlying Diophantine geometry guarantees that at least one of the available choices is good. The approach is described in detail for the important special case of the Golden code but it applies to a larger class of space-time codes where it provides a means of avoiding the uncertainties and implementation complexity associated with sphere decoding. In particular it extends battery life at the mobile terminal by eliminating the need for a second receive antenna. Simulation results for the Golden Code show performance within 2 dB of full maximum-likelihood decoding with worst case complexity that is quadratic in the size of the QAM signal constellation.