On the Construction of Polar Codes

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:
2011 Ieee International Symposium On Information Theory Proceedings (Isit), 11-15
Presented at:
IEEE International Symposium on Information Theory (ISIT), St Petersburg, RUSSIA, Jul 31-Aug 05, 2011
Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa

 Record created 2012-06-25, last modified 2018-01-28

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