Decoding algorithm and architecture for BCH codes under the Lee Metric

Abstract

The Lee metric measures the circular distance between two elements in a cyclic group and is particularly appropriate as a measure of distance for data transmission under phase-shift-keying modulation over a white noise channel. In this paper, using newly derived properties on Newton's identities, we initially investigate the Lee distance properties of a class of BCH codes and show that (for an appropriate range of parameters) their minimum Lee distance is at least twice their designed Hamming distance. We then make use of properties of these codes to devise an efficient algebraic decoding algorithm that successfully decodes within the above lower bound of the Lee error-correction capability. Finally, we propose an attractive design for the corresponding VLSI architecture that is only mildly more complex than popular decoder architectures under the Hamming metric; since the proposed architecture can also be used for decoding under the Hamming metric without extra hardware, one can use the proposed architecture to decode under both distance metrics (Lee and Hamming).