On the List Decodability of Matrix Codes with Different Metrics

Yang DING; Yuting QIU; Hongxi TONG

doi:10.1587/transfun.2021EAL2015

On the List Decodability of Matrix Codes with Different Metrics

Yang DING, Yuting QIU, Hongxi TONG

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One of the main problems in list decoding is to determine the tradeoff between the list decoding radius and the rate of the codes w.r.t. a given metric. In this paper, we first describe a “stronger-weaker” relationship between two distinct metrics of the same code, then we show that the list decodability of the stronger metric can be deduced from the weaker metric directly. In particular, when we focus on matrix codes, we can obtain list decodability of matrix code w.r.t. the cover metric from the Hamming metric and the rank metric. Moreover, we deduce a Johnson-like bound of the list decoding radius for cover metric codes, which improved the result of [20]. In addition, the condition for a metric that whether the list decoding radius w.r.t. this metric and the rate are bounded by the Singleton bound is presented.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E104-A No.10 pp.1430-1434

Publication Date: 2021/10/01

Publicized: 2021/03/29

Online ISSN: 1745-1337

DOI: 10.1587/transfun.2021EAL2015

Type of Manuscript: LETTER

Category: Coding Theory

Authors

Yang DING
  Shanghai University
Yuting QIU
  Shanghai University
Hongxi TONG
  Shanghai University

Keyword

list decoding, cover metric, rank metric, the Johnson radius, the Singleton bound

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Yang DING, Yuting QIU, Hongxi TONG, "On the List Decodability of Matrix Codes with Different Metrics" in IEICE TRANSACTIONS on Fundamentals, vol. E104-A, no. 10, pp. 1430-1434, October 2021, doi: 10.1587/transfun.2021EAL2015.
Abstract: One of the main problems in list decoding is to determine the tradeoff between the list decoding radius and the rate of the codes w.r.t. a given metric. In this paper, we first describe a “stronger-weaker” relationship between two distinct metrics of the same code, then we show that the list decodability of the stronger metric can be deduced from the weaker metric directly. In particular, when we focus on matrix codes, we can obtain list decodability of matrix code w.r.t. the cover metric from the Hamming metric and the rank metric. Moreover, we deduce a Johnson-like bound of the list decoding radius for cover metric codes, which improved the result of [20]. In addition, the condition for a metric that whether the list decoding radius w.r.t. this metric and the rate are bounded by the Singleton bound is presented.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/transfun.2021EAL2015/_p

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@ARTICLE{e104-a_10_1430,
author={Yang DING, Yuting QIU, Hongxi TONG, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={On the List Decodability of Matrix Codes with Different Metrics},
year={2021},
volume={E104-A},
number={10},
pages={1430-1434},
abstract={One of the main problems in list decoding is to determine the tradeoff between the list decoding radius and the rate of the codes w.r.t. a given metric. In this paper, we first describe a “stronger-weaker” relationship between two distinct metrics of the same code, then we show that the list decodability of the stronger metric can be deduced from the weaker metric directly. In particular, when we focus on matrix codes, we can obtain list decodability of matrix code w.r.t. the cover metric from the Hamming metric and the rank metric. Moreover, we deduce a Johnson-like bound of the list decoding radius for cover metric codes, which improved the result of [20]. In addition, the condition for a metric that whether the list decoding radius w.r.t. this metric and the rate are bounded by the Singleton bound is presented.},
keywords={},
doi={10.1587/transfun.2021EAL2015},
ISSN={1745-1337},
month={October},}

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TY - JOUR
TI - On the List Decodability of Matrix Codes with Different Metrics
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1430
EP - 1434
AU - Yang DING
AU - Yuting QIU
AU - Hongxi TONG
PY - 2021
DO - 10.1587/transfun.2021EAL2015
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E104-A
IS - 10
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - October 2021
AB - One of the main problems in list decoding is to determine the tradeoff between the list decoding radius and the rate of the codes w.r.t. a given metric. In this paper, we first describe a “stronger-weaker” relationship between two distinct metrics of the same code, then we show that the list decodability of the stronger metric can be deduced from the weaker metric directly. In particular, when we focus on matrix codes, we can obtain list decodability of matrix code w.r.t. the cover metric from the Hamming metric and the rank metric. Moreover, we deduce a Johnson-like bound of the list decoding radius for cover metric codes, which improved the result of [20]. In addition, the condition for a metric that whether the list decoding radius w.r.t. this metric and the rate are bounded by the Singleton bound is presented.
ER -