Achieving Close-Capacity Performance with Simple Concatenation Scheme on Multiple-Antenna Channels

Abstract

This paper proposes a simple yet capacity-approaching concatenation of a mixture of short memory length convolutional codes and simple rate-1 block code followed by either complex 1-dimensional (1-D) anti-Gray or Gray mapping over multiple antenna channels with quadrature phase-shift keying (QPSK). By interpreting rate-1 code together with 1-D mapping as a multi-D mapping employed over multiple transmit antennas, the error performance is analyzed in two regions, the error-floor and turbo pinch-off regions. In the former one, a tight union bound and design criterion on the asymptotic performance are first derived, which provide an useful tool to predict the error performance. Based on the design criterion, an optimal rate-1 code for each 1-D mapping is then constructed to achieve the best asymptotic performance. In the turbo pinch-off area, by using extrinsic information transfer (EXIT) chart, the most suitable mixed codes are selected for both symmetric and asymmetric antenna setups. It is demonstrated that the simple concatenation scheme can achieve near-capacity. Furthermore, its error performance is comparable to that obtained by using well-designed irregular low-density parity-check (LDPC) and repeat accumulate (RA) codes, and thereby, outperforms a scheme employing a parallel concatenated turbo code.