Math @ Duke

Publications [#322713] of Henry Pfister
Papers Published
 Pfister, HD; Urbanke, R, Nearoptimal finitelength scaling for polar codes over large alphabets,
IEEE International Symposium on Information Theory  Proceedings, vol. 2016August
(August, 2016),
pp. 215219, ISBN 9781509018062 [doi]
(last updated on 2018/03/20)
Abstract: © 2016 IEEE. For any prime power q, Mori and Tanaka introduced a family of qary polar codes based on q by q ReedSolomon polarization kernels. For transmission over a qary erasure channel, they also derived a closedform recursion for the erasure probability of each effective channel. In this paper, we use that expression to analyze the finitelength scaling of these codes on qary erasure channel with erasure probability ϵ ⋯ (0, 1). Our primary result is that, for any γ > 0 and δ > 0, there is a q 0 such that, for all q ≥ q 0 , the fraction of effective channels with erasure rate at most N γ is at least 1  ϵ  O(N 1/2+δ ), where N = q n is the blocklength. Since the gap to the channel capacity 1  ϵ cannot vanish faster than O(N1/2), this establishes nearoptimal finitelength scaling for this family of codes. Our approach can be seen as an extension of a similar analysis for binary polar codes by Mondelli, Hassani, and Urbanke.


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