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Decoding of Z 2 S Linear Generalized Kerdock Codes.
- Source :
-
Mathematics (2227-7390) . Feb2024, Vol. 12 Issue 3, p443. 17p. - Publication Year :
- 2024
-
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. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 22277390
- Volume :
- 12
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Mathematics (2227-7390)
- Publication Type :
- Academic Journal
- Accession number :
- 175370064
- Full Text :
- https://doi.org/10.3390/math12030443