Decoding of Z 2 S Linear Generalized Kerdock Codes

Aleksandar Minja () and Vojin Šenk
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Aleksandar Minja: Department of Power, Electronic and Telecommunication Engineering, Faculty of Engineering (Technical Sciences), University of Novi Sad, 21000 Novi Sad, Serbia
Vojin Šenk: Department of Power, Electronic and Telecommunication Engineering, Faculty of Engineering (Technical Sciences), University of Novi Sad, 21000 Novi Sad, Serbia

Mathematics, 2024, vol. 12, issue 3, 1-17

Abstract: 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.

Keywords: codes over rings; Kerdock codes; MAP decoding; Monte Carlo simulation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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