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Near-optimal finite-length scaling for polar codes over large alphabets

Publication ,  Conference
Pfister, HD; Urbanke, R
Published in: IEEE International Symposium on Information Theory - Proceedings
August 10, 2016

For any prime power q, Mori and Tanaka introduced a family of q-ary polar codes based on q by q Reed-Solomon polarization kernels. For transmission over a q-ary erasure channel, they also derived a closed-form recursion for the erasure probability of each effective channel. In this paper, we use that expression to analyze the finite-length scaling of these codes on q-ary erasure channel with erasure probability ϵ ⋯ (0, 1). Our primary result is that, for any γ > 0 and δ > 0, there is a q0 such that, for all q ≥ q0, the fraction of effective channels with erasure rate at most N-γ is at least 1 - ϵ - O(N-1/2+δ), where N = qn is the blocklength. Since the gap to the channel capacity 1 - ϵ cannot vanish faster than O(N-1/2), this establishes near-optimal finite-length 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.

Duke Scholars

Published In

IEEE International Symposium on Information Theory - Proceedings

DOI

ISSN

2157-8095

ISBN

9781509018062

Publication Date

August 10, 2016

Volume

2016-August

Start / End Page

215 / 219
 

Citation

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Pfister, H. D., & Urbanke, R. (2016). Near-optimal finite-length scaling for polar codes over large alphabets. In IEEE International Symposium on Information Theory - Proceedings (Vol. 2016-August, pp. 215–219). https://doi.org/10.1109/ISIT.2016.7541292
Pfister, H. D., and R. Urbanke. “Near-optimal finite-length scaling for polar codes over large alphabets.” In IEEE International Symposium on Information Theory - Proceedings, 2016-August:215–19, 2016. https://doi.org/10.1109/ISIT.2016.7541292.
Pfister HD, Urbanke R. Near-optimal finite-length scaling for polar codes over large alphabets. In: IEEE International Symposium on Information Theory - Proceedings. 2016. p. 215–9.
Pfister, H. D., and R. Urbanke. “Near-optimal finite-length scaling for polar codes over large alphabets.” IEEE International Symposium on Information Theory - Proceedings, vol. 2016-August, 2016, pp. 215–19. Scopus, doi:10.1109/ISIT.2016.7541292.
Pfister HD, Urbanke R. Near-optimal finite-length scaling for polar codes over large alphabets. IEEE International Symposium on Information Theory - Proceedings. 2016. p. 215–219.

Published In

IEEE International Symposium on Information Theory - Proceedings

DOI

ISSN

2157-8095

ISBN

9781509018062

Publication Date

August 10, 2016

Volume

2016-August

Start / End Page

215 / 219