Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/82171
Title: On List-Decodability of Random Rank Metric Codes and Subspace Codes
Authors: Ding, Yang
Keywords: Gilbert-Varshamov bound
Constant-dimension subspace codes
Issue Date: 2015
Source: Ding, Y. (2014). On List-Decodability of Random Rank Metric Codes and Subspace Codes. IEEE Transactions on Information Theory, 61(1), 51-59.
Series/Report no.: IEEE Transactions on Information Theory
Abstract: Codes in rank metric have a wide range of applications. To construct such codes with better list-decoding performance explicitly, it is of interest to investigate the listdecodability of random rank metric codes. It is shown that if n/m = b is a constant, then for every rank metric code in Fm×n q with rate R and list-decoding radius ρ must obey the Gilbert-Varshamov bound, that is, R ≤ (1-ρ)(1-bρ). Otherwise, the list size can be exponential and hence no polynomial-time list decoding is possible. On the other hand, for arbitrary 0 <; ρ <; 1 and E > 0, with E and ρ being independent of each other, with high probability, a random rank metric code with rate R = (1 - ρ)(1 - bρ) - can be efficiently list-decoded up to a fraction ρ of rank errors with constant list size O(1/E). We establish similar results for constant-dimension subspace codes. Moreover, we show that, with high probability, the list-decoding radius of random Fq-linear rank metric codes also achieve the Gilbert-Varshamov bound with constant list size O(exp(1/E)).
URI: https://hdl.handle.net/10356/82171
http://hdl.handle.net/10220/41145
ISSN: 0018-9448
DOI: 10.1109/TIT.2014.2371915
Rights: © 2014 IEEE.
Fulltext Permission: none
Fulltext Availability: No Fulltext
Appears in Collections:SPMS Journal Articles

SCOPUSTM   
Citations 10

21
Updated on Dec 28, 2021

PublonsTM
Citations 10

14
Updated on Mar 3, 2021

Page view(s)

245
Updated on Jun 27, 2022

Google ScholarTM

Check

Altmetric


Plumx

Items in DR-NTU are protected by copyright, with all rights reserved, unless otherwise indicated.