Attaining Capacity with iterated $(U |U + V )$ codes based on AG codes and Koetter-Vardy soft decoding

Abstract : 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.
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Communication dans un congrès
ISIT 2017 - IEEE International Symposium on Information Theory, Jun 2017, Aachen, Germany. IEEE, pp.6--10, 2017, 〈https://isit2017.org/〉. 〈10.1109/ISIT.2017.8006479〉
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Soumis le : mardi 12 décembre 2017 - 15:06:00
Dernière modification le : jeudi 26 avril 2018 - 10:27:44

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Irene Marquez-Corbella, Jean-Pierre Tillich. Attaining Capacity with iterated $(U |U + V )$ codes based on AG codes and Koetter-Vardy soft decoding. ISIT 2017 - IEEE International Symposium on Information Theory, Jun 2017, Aachen, Germany. IEEE, pp.6--10, 2017, 〈https://isit2017.org/〉. 〈10.1109/ISIT.2017.8006479〉. 〈hal-01661977〉

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