We present a low complexity iterative decoding method for a multiplexed Alamouti space-time code serially concatenated by a convolutional code. The space-time signalling code consists of a Gray coded 16-QAM mapper and two spatially overlaid Alamouti signalling blocks. A linear complexity decoder is used for decoding the inner space-time code. Ordinarily, an iterative decoding between the inner and outer decoders at the receiver does not improve performance when using a Gray coded modulation scheme. However we show that turbo gains are possible when a multiplexed Alamouti code is used. The low complexity inner decoder is based on Bayesian interference cancelling approach. We present a method of using both the extrinsic and full a posteriori values from the outer decoder to facilitate gains from iterations. The modified iterative decoder presented here favourably compares to a space-time bit interleaved coded modulation (ST-BICM) system providing the same spectral efficiency in terms of complexity-performance tradeoff.

Space-time codes built with multiplexed Alamouti components provide multiplexing as well as diversity gain. Their orthogonal structure also leads to simpler decoding algorithms. We consider a 4 × 2 system with multiplexed Alamouti codes. An exhaustive search maximum likelihood (ML) decoding for a 4×2 system is of order M4, for a modulation scheme with constellation size M. For multiplexed orthogonal designs, an exact fast ML decoding algorithm has recently been reported whose complexity order is M2for a 4 × 2 system with QAM constellations. Nevertheless, the quadratic complexity of this fast ML algorithm may still be infeasible in practice for large constellations (e.g. M ≥ 64 QAM). In this paper, we present a method for designing low complexity sub-optimal decoders based on a combination of search based ML decoding and linear decoding. Our formulation facilitates a direct investigation of the trade-off between performance and complexity. The complexity of our hybrid decoder is flexible and it can be fixed based on the desired performance for a hardware implementation. Although extendable to more general multiplexed Alamouti systems, we focus here on a 4 × 2 space-time-polarization system comprising of two dual-polarized transmit antennas and one dual-polarized receive antenna.

This paper deals witha posterioriprobability (APP) decoding of high-rate convolutional codes, using the dual code's trellis. After deriving the dual APP (DAPP) algorithm from the APP relation, its trellis-based implementation is addressed. The challenge involved in practical implementation of a DAPP decoder is then highlighted. Metric representation schemes similar to the log domain used for log-APP decoding are shown to be unattractive for DAPP decoding due to quantization requirements. After explaining the nature of the DAPP metrics, an arc hyperbolic tangent (AHT) scheme is proposed and its equivalent arithmetic operations derived. By using an efficient approximation, an addition is translated to an addition in the AHT domain. Efficient techniques for normalization and extrinsic log-likelihood ratio (LLR ) calculation are presented which reduce implementation complexity significantly. Simulation results with different high-rate codes are given to show that the AHT-DAPP decoder performs similarly to a log-APP decoder and at the same time performs better than a decoder for a punctured code. A fully fixed-point model of an AHT-DAPP decoder is shown to perform close to an optimum decoder. The decoding complexity of the log-APP and AHT-DAPP decoders are listed and compared for several rate-$k/(k+1)$codes. It is shown that an AHT-DAPP decoder starts to be less complex from a code rate of$7/8$. When compared against a max-log-APP decoder, the AHT-DAPP decoder is less complex at a code rate of$9/10$and above.

An a posteriori probability (APP) decoder working on the trellis of the dual code is preferred if the code rate is high. However, a hardware realisation of this decoder is quite complex due to very fine quantisation requirements. This paper explains the nature of the metrics in this dual-APP decoder and points out the underlying reason behind the unsuitability of a traditional log domain approach. We propose a new metric representation scheme and discuss the arithmetic operations involved for a trellis based implementation. Simulation results are given, showing a better performance tradeoff of the proposed scheme against quantisation