Bounds on the Probability of Undetected Error for q-Ary Codes

被引：0
|
作者：
Wang, Xuan [1 ]
Liu, Huizhou [2 ]
Sole, Patrick [3 ]
机构：
[1] Anhui Univ, Sch Math Sci, Hefei 230601, Peoples R China
[2] State Grid Anhui Elect Power Co Ltd, Hefei 230601, Peoples R China
[3] Aix Marseille Univ, CNRS, I2M, Cent Marseille, F-13009 Marseilles, France
来源：
ENTROPY | 2023年 / 25卷 / 09期
关键词：
error correcting codes; probability of undetected error; linear programmming; DISTANCE DISTRIBUTION; BINOMIAL MOMENTS; PROPER;
D O I：
10.3390/e25091349
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
We study the probability of an undetected error for general q-ary codes. We give upper and lower bounds on this quantity, by the Linear Programming and the Polynomial methods, as a function of the length, size, and minimum distance. Sharper bounds are obtained in the important special case of binary Hamming codes. Finally, several examples are given to illustrate the results of this paper.
引用
收藏
页数：17
相关论文
共 50 条
  • [41] ON (Q,1)-SUBNORMAL Q-ARY COVERING CODES
    HONKALA, I
    DISCRETE APPLIED MATHEMATICS, 1994, 52 (03) : 213 - 221
  • [42] Algorithms for q-ary error-correcting codes with limited magnitude and feedback
    Deppe, Christian
    Lebedev, Vladimir
    DISCRETE MATHEMATICS, 2021, 344 (02)
  • [43] Optimal two-level q-ary unequal error control codes
    Kaneko, H
    Fujiwara, E
    2003 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY - PROCEEDINGS, 2003, : 215 - 215
  • [44] Polar Codes for Q-ary Source Coding
    Karzand, Mohammad
    Telatar, Emre
    2010 IEEE INTERNATIONAL SYMPOSIUM ON INFORMATION THEORY, 2010, : 909 - 912
  • [45] Matched filter bounds on q-ary QAM symbol error probability for diversity receptions and multipath fading ISI channels
    Lee, HN
    Pottie, GJ
    PIMRC 2000: 11TH IEEE INTERNATIONAL SYMPOSIUM ON PERSONAL, INDOOR AND MOBILE RADIO COMMUNICATIONS, VOLS 1 AND 2, PROCEEDINGS, 2000, : 577 - 583
  • [46] A Class of q-Ary Unidirectional Error Correcting Codes for MLC Flash Memories
    Kotaki, Shohei
    Kitakami, Masato
    2013 IEEE 19TH PACIFIC RIM INTERNATIONAL SYMPOSIUM ON DEPENDABLE COMPUTING (PRDC 2013), 2013, : 132 - 133
  • [47] Synchronizing codewords of q-ary Huffman codes
    Perkins, S
    Escott, AE
    DISCRETE MATHEMATICS, 1999, 197 (1-3) : 637 - 655
  • [48] Classification of q-Ary Perfect Quantum Codes
    Li, Zhuo
    Xing, Lijuan
    IEEE TRANSACTIONS ON INFORMATION THEORY, 2013, 59 (01) : 631 - 634
  • [49] QAM modulations with q-ary turbo codes
    张豫伟
    王新梅
    Science China Technological Sciences, 1997, (01) : 64 - 70
  • [50] QAM modulations with q-ary turbo codes
    Zhang, YW
    Wang, XM
    SCIENCE IN CHINA SERIES E-TECHNOLOGICAL SCIENCES, 1997, 40 (01): : 64 - 70
12345