TY - GEN

T1 - Locally Balanced Constraints

AU - Gabrys, Ryan

AU - Kiah, Han Mao

AU - Vardy, Alexander

AU - Yaakobi, Eitan

AU - Zhang, Yiwei

N1 - Publisher Copyright: © 2020 IEEE.

PY - 2020/6

Y1 - 2020/6

N2 - Three new constraints are introduced in this paper. These constraints are characterized by limitations on the Hamming weight of every subword of some fixed even length l. In the (l, δ)-locally-balanced constraint, the Hamming weight of every length-l subword is bounded between l/2 - δ and l/2 + δ. The strong-(l,δ)-locally-balanced constraint imposes the locally- balanced constraint for any subword whose length is at least l. Lastly, the Hamming weight of every length-l subword which satisfies the (l, δ)-locally-bounded constraint is at most l/2 - δ. It is shown that the capacity of the strong-(l, δ)-locally-balanced constraint does not depend on the value of l and is identical to the capacity of the (2δ + 1)-RDS constraint. The latter constraint limits the difference between the number of zeros and ones in every prefix of the word to be at most 2δ + 1. This value is also a lower bound on the capacity of the (l, δ)-locally-balanced constraint, while a corresponding upper bound is given as well. Lastly, it is shown that if δ is not large enough, namely for δ < l/2, then the capacity of the (l, δ)-locally-bounded constraint approaches 1 as l increases.

AB - Three new constraints are introduced in this paper. These constraints are characterized by limitations on the Hamming weight of every subword of some fixed even length l. In the (l, δ)-locally-balanced constraint, the Hamming weight of every length-l subword is bounded between l/2 - δ and l/2 + δ. The strong-(l,δ)-locally-balanced constraint imposes the locally- balanced constraint for any subword whose length is at least l. Lastly, the Hamming weight of every length-l subword which satisfies the (l, δ)-locally-bounded constraint is at most l/2 - δ. It is shown that the capacity of the strong-(l, δ)-locally-balanced constraint does not depend on the value of l and is identical to the capacity of the (2δ + 1)-RDS constraint. The latter constraint limits the difference between the number of zeros and ones in every prefix of the word to be at most 2δ + 1. This value is also a lower bound on the capacity of the (l, δ)-locally-balanced constraint, while a corresponding upper bound is given as well. Lastly, it is shown that if δ is not large enough, namely for δ < l/2, then the capacity of the (l, δ)-locally-bounded constraint approaches 1 as l increases.

UR - http://www.scopus.com/inward/record.url?scp=85090417716&partnerID=8YFLogxK

U2 - https://doi.org/10.1109/ISIT44484.2020.9173933

DO - https://doi.org/10.1109/ISIT44484.2020.9173933

M3 - منشور من مؤتمر

T3 - IEEE International Symposium on Information Theory - Proceedings

SP - 664

EP - 669

BT - 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings

T2 - 2020 IEEE International Symposium on Information Theory, ISIT 2020

Y2 - 21 July 2020 through 26 July 2020

ER -