Decoding of Z 2 S Linear Generalized Kerdock Codes.

Many families of binary nonlinear codes (e.g., Kerdock, Goethals, Delsarte–Goethals, Preparata) can be very simply constructed from linear codes over the Z 4 ring (ring of integers modulo 4), by applying the Gray map to the quaternary symbols. Generalized Kerdock codes represent an extension of classical Kerdock codes to the Z 2 S ring. In this paper, we develop two novel soft-input decoders, designed to exploit the unique structure of these codes. We introduce a novel soft-input ML decoding algorithm and a soft-input soft-output MAP decoding algorithm of generalized Kerdock codes, with a complexity of O (N S log 2 N) , where N is the length of the Z 2 S code, that is, the number of Z 2 S symbols in a codeword. Simulations show that our novel decoders outperform the classical lifting decoder in terms of error rate by some 5 dB. [ABSTRACT FROM AUTHOR]