Fast optimal decoding of multiplexed orthogonal designs by conditional optimization
This paper focuses on conditional optimization as a decoding primitive for high rate spacetime codes that are obtained by multiplexing in the spatial and code domains. The approach is a crystallization of the work of Hottinen which applies to spacetime codes that are assisted by quasi-orthogonality. It is independent of implementation and is more general in that it can be applied to spacetime codes such as the Golden Code and perfect spacetime block codes, that are not assisted by quasi-orthogonality, to derive fast decoders with essentially maximum likelihood (ML) performance. The conditions under which conditional optimization leads to reduced complexity ML decoding are captured in terms of the induced channel at the receiver. These conditions are then translated back to the transmission domain leading to codes that are constructed by multiplexing orthogonal designs. The methods are applied to several block spacetime codes obtained by multiplexing Alamouti blocks where it leads to ML decoding with complexity O(N2) where $N$ is the size of the underlying QAM signal constellation. A new code is presented that tests commonly accepted design principles and for which decoding by conditional optimization is both fast and ML. The two design principles for perfect spacetime codes are nonvanishing determinant of pairwise differences and cubic shaping, and it is cubic shaping that restricts the possible multiplexing structures. The new code shows that it is possible to give up on cubic shaping without compromising code performance or decoding complexity. © 2006 IEEE.
Sirianunpiboon, S; Wu, Y; Calderbank, AR; Howard, SD
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