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On the construction of polar codes

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4 Author(s)
Pedarsani, R. ; Sch. of Comput. & Commun. Syst., EPFL, Lausanne, Switzerland ; Hassani, S.H. ; Tal, I. ; Telatar, I.E.

We consider the problem of efficiently constructing polar codes over binary memoryless symmetric (BMS) channels. The complexity of designing polar codes via an exact evaluation of the polarized channels to find which ones are “good” appears to be exponential in the block length. In [3], Tal and Vardy show that if instead the evaluation if performed approximately, the construction has only linear complexity. In this paper, we follow this approach and present a framework where the algorithms of [3] and new related algorithms can be analyzed for complexity and accuracy. We provide numerical and analytical results on the efficiency of such algorithms, in particular we show that one can find all the “good” channels (except a vanishing fraction) with almost linear complexity in block-length (except a polylogarithmic factor).

Published in:

Information Theory Proceedings (ISIT), 2011 IEEE International Symposium on

Date of Conference:

July 31 2011-Aug. 5 2011