Comparing decoding methods for quaternary linear codes

Abstract

Permutation decoding is a technique which involves finding a subset S, called PDset, of the permutation automorphism group of a code C. Constructions of small PD-sets for partial decoding for two families of Z 4-linear codes (Hadamard and Kerdock) are given. Moreover, different decoding methods for Z 4-linear codes are compared by showing their performance applied to these two families.

Decoding of Z2S Linear Generalized Kerdock Codes

“…A variety of strategies have been used in designing decoders for codes over rings, as mentioned in [25]. These include the algebraic (syndrome) decoding approach [26], the lifting decoder technique, introduced in [27] and extended in [28], the coset decomposition approach [29], and the permutation decoding [25,30,31]. Several algebraic decoders of codes over rings were presented in [2,[32][33][34][35].…”

SISO Decoding of ℤ4 Linear Kerdock and Preparata Codes

“…Common approaches for designing decoders for codes over rings include [23] the algebraic (syndrome) decoding of linear codes [24], the lifting decoder technique [25,26], the partitioning of a code into the subcode and its cosets (a.k.a. the coset decomposition approach), introduced by Conway and Sloane in [27] (which works for both linear and nonlinear codes), and the permutation decoding [23,28,29]. Most of the soft decision decoders employ some form of the coset decomposition approach.…”