Improved Max-Log-MAP Turbo Decoding by Maximization of Mutual Information Transfer

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Improved Max-Log-MAP Turbo Decoding by Maximization of Mutual Information Transfer Holger Claussen Signals & Systems Group, University of Edinburgh, Edinburgh EH9 3JL, UK Email: [email protected]; [email protected]

Hamid Reza Karimi Bell Laboratories, Lucent Technologies, Swindon SN5 7DJ, UK Email: [email protected]

Bernard Mulgrew Signals & Systems Group, University of Edinburgh, Edinburgh EH9 3JL, UK Email: [email protected] Received 1 October 2003; Revised 7 May 2004 The demand for low-cost and low-power decoder chips has resulted in renewed interest in low-complexity decoding algorithms. In this paper, a novel theoretical framework for improving the performance of turbo decoding schemes that use the max-logMAP algorithm is proposed. This framework is based on the concept of maximizing the transfer of mutual information between the component decoders. The improvements in performance can be achieved by using optimized iteration-dependent correction weights to scale the a priori information at the input of each component decoder. A method for the offline computation of the correction weights is derived. It is shown that a performance which approaches that of a turbo decoder using the optimum MAP algorithm can be achieved, while maintaining the advantages of low complexity and insensitivity to input scaling inherent in the max-log-MAP algorithm. The resulting improvements in convergence of the turbo decoding process and the expedited transfer of mutual information between the component decoders are illustrated via extrinsic information transfer (EXIT) charts. Keywords and phrases: turbo decoding, max-log-MAP, correction weights, EXIT charts, mutual information.

1.

INTRODUCTION

Since the discovery of turbo codes [1], there has been renewed interest in the field of coding theory, with the aim of approaching the Shannon limit. Furthermore, with the proliferation of wireless mobile devices in recent years, the availability of low-cost and low-power decoder chips is of paramount importance. To this end, several techniques for reducing the complexity of the optimum MAP decoding algorithm [2] have been proposed. Examples include the logMAP, max-log-MAP, and SOVA algorithms [3, 4, 5]. In the case of the latter two algorithms, the reduction in complexity is accompanied by some degradation in error correction performance. This issue has been addressed by a number of authors in the context of turbo decoding schemes. In [6], the performance degradation caused by the SOVA algorithm is attributed to an incorrect scaling of the extrinsic information, in addition, to nonzero correlation between the intrinsic and extrinsic information at the component

decoder outputs. Performance improvements were demonstrated through the use of correction factors computed as a function of soft-output statistics of the component decoders. The degradation caused by the max-log-MAP algorithm was addressed in [7, 8]. Performance gains were achieved by scaling of the extrinsic information at the component decoder outputs. The value o