Distributed totally decomposed cumulative Goppa coded-cooperative communication with optimized selection in the relay

Abstract

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Cooperative H-ARQ employing powerful totally decomposed cumulative Goppa codes

“…Goppa codes, introduced by Goppa [10], are an important class of FEC codes. They can be categorized into four subclasses based on the form of a Goppa polynomial: cyclic codes, separable codes, irreducible codes, and cumulative Goppa codes [16]. The definition of a specific type of Goppa code known as the TDCG code involves choosing a polynomial G(x) = (x − α) s and a subset L ⊆ F q \ {α : G(α) = 0}, where s denotes the order of cumulativity [16], [15].…”