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Construction and soft-in/soft-out decoding of recursive codes based on the Plotkin-construction over arbitrary finite sets

In this paper, we investigate the applicability of the Plotkin code construction method to arbitrary finite sets, particularly complex valued modulation alphabets. Furthermore, we derive a recursive soft-in/soft-out decoding algorithm for these code constructions. The purpose is to have an encoding/decoding scheme available, which uses elements of finite sets-especially the complex valued elements of modulation alphabets-directly as information symbols. Simulations for some simple code constructions show the flexibility and performance of that codes and the proposed decoding algorithm.