Polar Codes with Higher-Order Memory
- 作者: Afşer H.1,2, Deliç H.1
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隶属关系:
- Wireless Communications Laboratory, Department of Electrical and Electronics Engineering
- Department of Electrical and Electronics Engineering
- 期: 卷 54, 编号 4 (2018)
- 页面: 301-328
- 栏目: Coding Theory
- URL: https://journal-vniispk.ru/0032-9460/article/view/166548
- DOI: https://doi.org/10.1134/S0032946018040014
- ID: 166548
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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(n − m), 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) = ρm − ρm − 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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