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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Submitted on : Tuesday, December 12, 2017 - 3:06:00 PM
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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. pp.6--10, ⟨10.1109/ISIT.2017.8006479⟩. ⟨hal-01661977⟩

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