期刊
IEEE TRANSACTIONS ON INFORMATION THEORY
卷 67, 期 10, 页码 6384-6394出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TIT.2021.3069446
关键词
Deletion codes; list decoding; explicit constructions
资金
- NSF [CCF-1814603]
- Simons Investigator Award
- Knut and Alice Wallenberg Foundation
The study provides a constructive method for correcting errors in binary codes after deleting two bits, and explicitly determines the size of the codes. The existence of such codes was previously unclear.
We give an explicit construction of length-n binary codes capable of correcting the deletion of two bits that have size 2(n)/n(4+o(1)). This matches up to lower order terms the existential result, based on an inefficient greedy choice of codewords, that guarantees such codes of size Omega(2(n)/n(4)). Our construction is based on augmenting the classic Varshamov-Tenengolts construction of single deletion codes with additional check equations. We also give an explicit construction of binary codes of size Omega(2(n)/n(3+o(1))) that can be list decoded from two deletions using lists of size two. Previously, even the existence of such codes was not clear.
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