Polar Codes with Higher-Order Memory


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详细

We introduce a construction of a set of code sequences {Cn(m) : n ≥ 1, m ≥ 1} with memory order m and code length N(n). {Cn(m)} is a generalization of polar codes presented by Arıkan in [1], where the encoder mapping with length N(n) is obtained recursively from the encoder mappings with lengths N(n − 1) and N(nm), and {Cn(m)} coincides with the original polar codes when m = 1. We show that {Cn(m)} achieves the symmetric capacity I(W) of an arbitrary binary-input, discrete-output memoryless channel W for any fixed m. We also obtain an upper bound on the probability of block-decoding error Pe of {Cn(m)} and show that \({P_e} = O({2^{ - {N^\beta }}})\) is achievable for β < 1/[1+m(ϕ − 1)], where ϕ ∈ (1, 2] is the largest real root of the polynomial F(m, ρ) = ρmρm − 1 − 1. The encoding and decoding complexities of {Cn(m)} decrease with increasing m, which proves the existence of new polar coding schemes that have lower complexity than Arıkan’s construction.

作者简介

H. Afşer

Wireless Communications Laboratory, Department of Electrical and Electronics Engineering; Department of Electrical and Electronics Engineering

编辑信件的主要联系方式.
Email: huseyin.afser@boun.edu.tr
土耳其, Istanbul; Adana

H. Deliç

Wireless Communications Laboratory, Department of Electrical and Electronics Engineering

Email: huseyin.afser@boun.edu.tr
土耳其, Istanbul

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