Attaining Capacity with iterated $(U |U + V )$ codes based on AG codes and Koetter-Vardy soft decoding
Résumé
In this paper we show how to attain the capacity of discrete symmetric channels with polynomial time decoding complexity by considering iterated (U | U + V) constructions with algebraic geometry (AG) code components. These codes are decoded with a recursive computation of the a posteriori probabilities of the code symbols together with decoding the AG components with the Koetter-Vardy algorithm. We show that, when the number of levels of the iterated (U | U + V) construction tends to infinity, we attain the capacity of any discrete symmetric channel. Moreover the error probability decays quasi-exponentially with the codelength in the case of Reed-Solomon code constituents and exponentially with Tsfasman-Vl˘ aduts-Zink code constituents.
Domaines
Théorie de l'information [cs.IT]
Origine : Fichiers produits par l'(les) auteur(s)
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