Iterative decoding of space-time-frequency block coded mimo concatenated with LDPH codes

Abstract

In this dissertation the aim was to investigate the usage of algorithms found in computer science and apply suitable algorithms to the problem of decoding multiple-input multipleoutput (MIMO) space-time-frequency block coded signals. It was found that the sphere decoder is a specific implementation of the A* tree search algorithm that is well known in computer science. Based on this knowledge, the sphere decoder was extended to include a priori information in the maximum a posteriori probability (MAP) joint decoding of the STFC block coded MIMO signals. The added complexity the addition of a priori information has on the sphere decoder was investigated and compared to the sphere decoder without a priori information. To mitigate the potential additional complexity several algorithms that determine the order in which the symbols are decoded were investigated. Three new algorithms incorporating a priori information were developed and compared with two existing algorithms. The existing algorithms compared against are sorting based on the norms of the channel matrix columns and the sorted QR decomposition. Additionally, the zero forcing (ZF) and minimum mean squared error (MMSE) decoderswith and without decision feedback (DF) were also extended to include a priori information. The developed method of incorporating a priori information was compared to an existing algorithm based on receive vector translation (RVT). The limitation of RVT to quadrature phase shift keying (QPSK) and binary shift keying (BPSK) constellations was also shown in its derivation. The impact of the various symbol sorting algorithms initially developed for the sphere decoder on these decoders was also investigated. The developed a priori decoders operate in the log domain and as such accept a priori information in log-likelihood ratios (LLRs). In order to output LLRs to the forward error correcting (FEC) code, use of the max-log approximation, occasionally referred to as hard-to-soft decoding, was made. In order to test the developed decoders, an iterative turbo decoder structure was used together with an LDPC decoder to decode threaded algebraic space-time (TAST) codes in a Rayleigh faded MIMO channel. Two variables that have the greatest impact on the performance of the turbo decoder were identified: the hard limit value of the LLRs to the LDPC decoder and the number of independently faded bits in the LDPC code.