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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)).
ISSN: 0018-9448
DOI: 10.1109/TIT.2014.2371915
Rights: © 2014 IEEE.
Fulltext Permission: none
Fulltext Availability: No Fulltext
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