Nonlinear hierarchical space-time block codes

Recent designs for space-time block codes (STBCs) have exploited the structure of the codes (unitary, orthogonal) to enable systematic construction. Code sets found by exhaustive search to optimize cost functions can often achieve performance gains of several dB; however, such searches are not feasible for large block or constellation sizes. In this work, properties of searched codes are determined which suggest a systematic code construction method. The results are nonlinear hierarchical codes (NHCs), where coding gain is optimized at each layer of the hierarchy and codes of arbitrary block-sizes/constellations can be designed. A fundamental difference between the structured codes (unitary, orthogonal) and NHCs is that in NHCs, the relationship between codeword is manipulated rather than properties of the individual codeword. The proposed scheme is essentially a generalization of Slepian´s group codes for the Gaussian channel to the multiple-input multiple-output quasistatic fading channel.