TY - JOUR
T1 - Uncertainty of reconstruction with list-decoding from uniform-tandem-duplication noise
AU - Yehezkeally, Yonatan
AU - Schwartz, Moshe
N1 - Funding Information:
Manuscript received March 3, 2020; revised October 23, 2020; accepted February 17, 2021. Date of publication April 1, 2021; date of current version June 16, 2021. This work was supported in part by the Israel Science Foundation (ISF) under Grant 270/18. This article was presented in part at the 2020 International Symposium on Information Theory. (Corresponding author: Yonatan Yehezkeally.) Yonatan Yehezkeally was with the School of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beer Sheva 8410501, Israel. He is now with the Institute for Communications Engineering, Technical University of Munich, 80333 Munich, Germany (e-mail: yonatan.yehezkeally@tum.de).
Publisher Copyright:
© 1963-2012 IEEE.
PY - 2021/7/1
Y1 - 2021/7/1
N2 - We propose a list-decoding scheme for reconstruction codes in the context of uniform-tandem-duplication noise, which can be viewed as an application of the associative memory model to this setting. We find the uncertainty associated with m>2 strings (where a previous paper considered m=2 ) in asymptotic terms, where code-words are taken from an error-correcting code. Thus, we find the trade-off between the design minimum distance, the number of errors, the acceptable list size and the resulting uncertainty, which corresponds to the required number of distinct retrieved outputs for successful reconstruction. It is therefore seen that by accepting list-decoding one may decrease coding redundancy, or the required number of reads, or both.
AB - We propose a list-decoding scheme for reconstruction codes in the context of uniform-tandem-duplication noise, which can be viewed as an application of the associative memory model to this setting. We find the uncertainty associated with m>2 strings (where a previous paper considered m=2 ) in asymptotic terms, where code-words are taken from an error-correcting code. Thus, we find the trade-off between the design minimum distance, the number of errors, the acceptable list size and the resulting uncertainty, which corresponds to the required number of distinct retrieved outputs for successful reconstruction. It is therefore seen that by accepting list-decoding one may decrease coding redundancy, or the required number of reads, or both.
KW - DNA storage
KW - List decoding
KW - Reconstruction
KW - String-duplication systems
UR - http://www.scopus.com/inward/record.url?scp=85103799336&partnerID=8YFLogxK
U2 - 10.1109/TIT.2021.3070466
DO - 10.1109/TIT.2021.3070466
M3 - Article
AN - SCOPUS:85103799336
SN - 0018-9448
VL - 67
SP - 4276
EP - 4287
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 7
M1 - 9393394
ER -