On the Polarizing Behavior and Scaling Exponent of Polar Codes with Product Kernels

被引:0
|
作者
Bhandari, Manan [1 ]
Bansal, Ishan [1 ]
Lalitha, V [1 ]
机构
[1] Int Inst Informat Technol Hyderabad, SPCRC, Hyderabad, India
关键词
D O I
10.1109/ncc48643.2020.9056096
中图分类号
TN [电子技术、通信技术];
学科分类号
0809 ;
摘要
Polar codes, introduced by Arikan, achieve the capacity of arbitrary binary-input discrete memoryless channel W under successive cancellation decoding. Any such channel having capacity I(W) and for any coding scheme allowing transmission at rate R, scaling exponent is a parameter which characterizes how fast gap to capacity decreases as a function of code length N for a fixed probability of error. The relation between them is given by N >= alpha/(I(W) - R)(mu). Scaling exponent for kernels of small size up to L = 8 have been exhaustively found. In this paper, we consider product kernels T-L, obtained by taking Kronecker product of component kernels. We derive the properties of polarizing product kernels relating to number of product kernels, self duality and partial distances in terms of the respective properties of the smaller component kernels. Subsequently, polarization behavior of component kernel T-l is used to calculate scaling exponent of T-L = T-2 circle times T-l. Using this method, we show that mu(T-2 circle times T-5) = 3.942. Further, we employ a heuristic approach to construct good kernel of L = 14 from kernel having size l = 8 having best mu and find mu(T-2 circle times T-7) = 3.485.
引用
收藏
页数:6
相关论文
共 50 条
  • [1] Explicit Polar Codes with Small Scaling Exponent
    Yao, Hanwen
    Fazeli, Arman
    Vardy, Alexander
    [J]. 2019 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY (ISIT), 2019, : 1757 - 1761
  • [2] Sub-4.7 Scaling Exponent of Polar Codes
    Wang, Hsin-Po
    Lin, Ting-Chun
    Vardy, Alexander
    Gabrys, Ryan
    [J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2023, 69 (07) : 4235 - 4254
  • [3] Scaling Exponent of List Decoders with Applications to Polar Codes
    Mondelli, Marco
    Hassani, S. Hamed
    Urbanke, Ruediger
    [J]. 2013 IEEE INFORMATION THEORY WORKSHOP (ITW), 2013,
  • [4] Scaling Exponent of List Decoders With Applications to Polar Codes
    Mondelli, Marco
    Hassani, S. Hamed
    Urbanke, Rudiger L.
    [J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2015, 61 (09) : 4838 - 4851
  • [5] Unified Scaling of Polar Codes: Error Exponent, Scaling Exponent, Moderate Deviations, and Error Floors
    Mondelli, Marco
    Hassani, S. Hamed
    Urbanke, Rudiger L.
    [J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2016, 62 (12) : 6698 - 6712
  • [6] Unified Scaling of Polar Codes: Error Exponent, Scaling Exponent, Moderate Deviations, and Error Floors
    Mondelli, Marco
    Urbanke, Rudiger
    Hassani, S. Hamed
    [J]. 2015 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY (ISIT), 2015, : 1422 - 1426
  • [7] Binary Linear Codes With Optimal Scaling: Polar Codes With Large Kernels
    Fazeli, Arman
    Hassani, Hamed
    Mondelli, Marco
    Vardy, Alexander
    [J]. IEEE TRANSACTIONS ON INFORMATION THEORY, 2021, 67 (09) : 5693 - 5710
  • [8] Binary Linear Codes with Optimal Scaling: Polar Codes with Large Kernels
    Fazeli, Arman
    Hassani, Hamed
    Mondelli, Marco
    Vardy, Alexander
    [J]. 2018 IEEE INFORMATION THEORY WORKSHOP (ITW), 2018, : 395 - 399
  • [9] The Penalty in Scaling Exponent for Polar Codes is Analytically Approximated by the Golden Ratio
    Shental, Ori
    [J]. 2019 IEEE GLOBAL COMMUNICATIONS CONFERENCE (GLOBECOM), 2019,
  • [10] Scaling Exponent and Moderate Deviations Asymptotics of Polar Codes for the AWGN Channel
    Fong, Silas L.
    Tan, Vincent Y. E.
    [J]. ENTROPY, 2017, 19 (07)