A performance study of a genetic algorithm based mapper design for uncoded space-time labeling diversity

The extent to which uncoded space-time labeling diversity (USTLD) achieves labeling diversity (LD) depends on the binary mappers used to encode information codewords. Current mapper design algorithms are constrained to constellations of modulation order M=16 due to the high computational costs involved. To reduce the computational costs, a genetic algorithm (GA) implementation had been proposed to design LD mappers irrespective of constellation shape or size. Current literature based on designing LD mappers using the GA has not been exhaustively tested for high-density constellations. This article applies the high-density mappers to the GA that will produce matching or improved LD mapper designs. Additionally, the GA is analyzed and compared to existing algorithmic approaches that produce LD mappers. The GA had produced high-density M-QAM mapper designs that match but did not improve upon existing heuristic and algorithmic mapper designs. In the case of high-density M-PSK constellations, the 64-PSK, 128-PSK, and 256-PSK constellations exhibited diversity gains of approximately 5, 4, and 8 dB over existing heuristic mapper designs while exhibiting gains of approximately 9, 7, and 10 dB over the Alamouti STBC at the BER of 10-6, respectively. The 128-APSK and 256-APSK mappers produced by the GA exhibited diversity gains of approximately 3 and 6 dB over existing mapper designs and approximately 7 and 12 dB over the Alamouti STBC at the BER of 10-6. The GA produced LD mapper designs for asymmetric 32-APSK, 64-APSK, 128-APSK, and 256-APSK constellations. These constellations exhibited diversity gains of approximately 5, 17, 5, and 5 dB over the Alamouti STBC, respectively. The GA was found to produce mapper designs that match or improve upon existing heuristic and algorithmic approaches. A computational complexity analysis was performed on the GA, to which the GA was found to have a complexity of O(M2). This was exponentially less expensive than exhaustive search and branch-and-bound QAP solvers.