Optimal Generation of Space–Time Trellis Codes via Coset Partitioning

Abstract

Criteria to design good space-time trellis codes (STTCs) have been already developed in previous publications. However, the computation of the best STTCs is time-consuming because a long exhaustive or systematic computing search is required, especially for a high number of states and/or transmit antennas. In order to reduce the search time, an efficient method must be employed to generate the STTCs with the best performance. In this paper, a technique called coset partitioning is proposed to design easily and efficiently optimal 2 n -PSK STTCs with any number of transmit antennas. The coset partitioning is an improved extension to multiple input multiple output (MIMO) systems of the set partitioning proposed by Ungerboeck. This extension is based on the lattice and coset Calderbank's approach. With this method, optimal blocks of the generator matrix are obtained for 4-PSK and 8-PSK codes. These optimal blocks lead to the generation of the STTCs with the best Euclidean distances between the codewords. Thus, new codes are proposed with 3 to 6 transmit antennas for 4-PSK modulation and with 3 and 4 transmit antennas for 8-PSK modulation. These new codes outperform the corresponding best known codes. Besides, the first 4-PSK STTCs with 7 and 8 transmit antennas and the first 8-PSK STTCs with 5 and 6 transmit antennas are given and their performance is evaluated by simulation.

QPSK super-orthogonal space-time trellis codes with 3 and 4 transmit antennas

“…As shown for SO-STTCs with 2 transmit antennas in [15] and for STTCs in [3], the generator matrix can be divided into blocks of columns.…”

“…Thus, the last block and the block relative to the parallel branches must generate the group Z n S 4 . The method to select the columns of generator matrix to obtain a subgroup is presented in [3]. The best codes are combinations of the created blocks.…”

“…The performance of each new code is evaluated by simulation in a slow Rayleigh fading channel and compared to the performance of the corresponding STTC in Table II proposed in [3]. For the simulation, the channel fading coefficients are independent samples of a complex Gaussian process with zero mean and variance 0.5 per dimension.…”

“…Chen et al proposed in [2] the trace criterion to improve the coding gain of STTCs. Based on these criteria, a method called coset partitioning has been proposed in [3] to obtain efficiently the best STTCs.…”

“…In this paper, we propose to extend the matrix representation of SO-STTCs [9] for 3 and 4 transmit antennas. This representation allows to design efficiently SO-STTCs, thanks to the coset partitioning [3]. Thus, new SO-STTCs with 3 and 4 transmit antennas are proposed.…”