Cognitive decoding and the golden code

Space time signal processing starts with a system of linear equations where signals are multiplied by channel gains, and the standard criteria for the design of space time codes focus on differences between codewords at the transmitter. The value of algebraic constructions is to transfer structure (correlation) at the transmitter to structure at the receiver, and the focus of this paper is the induced channel at the receiver. We use the Golden code to explore the idea of introducing structure at the transmitter to enable low complexity decoding at the receiver. This is an important special case, since the Golden code is incorporated in the IEEE 802.16 standard, but the value of our approach is not limited to this example. We describe a cognitive decoder for the Golden code with complexity O(N²) that comes within 3dB of full MAP/ML decoding. The decoder is cognitive in that it uses channel state information to choose between two algorithms in a way that is independent of the signal-to-noise ratio. The primary algorithm is interference cancellation which fails to perform well on a proportion of channels. We identify the channel conditions for which interference cancellation fails and show that for these channels the decoding problem effectively reduces to a single receive antenna decoding problem for which we have developed an efficient zero forcing algorithm. Previous hybrid approaches based on sphere decoding have cubic worst case complexity and employ decision rules based on condition number of the posterior covariance matrix. Interference cancellation is different in that orientation of the covariance matters. The cognitive decoder for the Golden code provides a uniform solution to different wireless environments (Rayleigh/Rician) that combine rich scattering and line of sight components. The gap between cognitive and full MAP/ML decoding reduces to essentially ML performance as the line of sight component becomes more dominant.