Soft-Decision Decoding of Linear Block Codes Using Preprocessing and Diversification

Abstract

Order-w reprocessing is a suboptimal soft-decision decoding approach for binary linear block codes in which up to w bits are systematically flipped on the so-called most reliable (information) basis (MRB). This correspondence first incorporates two preprocessing rules into order-w reprocessing and shows that, with appropriate choice of parameters, the proposed order-w reprocessing with preprocessing requires comparable complexity to order-w reprocessing but achieves asymptotically the performance of order-(w+2) reprocessing. To complement the MRB, a second basis is employed for practical SNRs and this approach is systematically extended to a multibasis order-w reprocessing scheme for high signal-to-noise ratios (SNRs). It is shown that the proposed multibasis scheme significantly enlarges the error-correction radius, a commonly used measure of performance at high SNRs, over the original (single-basis) order-w reprocessing. As a by-product, this approach also precisely characterizes the asymptotic performance of the well-known Chase and generalized minimum distance (GMD) decoding algorithms. The proposed algorithm successfully decodes the (192,96) Reed-Solomon concatenated code and the (256,147) extended BCH code in near optimal manner (within 0.01 dB at a block-error rate of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> ) with affordable computational cost