Technical Program

Paper Detail

Paper IDM.5.2
Paper Title Locally Balanced Constraints
Authors Ryan Gabrys, UCSD, United States; Han Mao Kiah, NTU, Singapore; Alexander Vardy, UCSD, United States; Eitan Yaakobi, Yiwei Zhang, Technion - Israel Institute of Technology, Israel
Session M.5: Coding for Storage and Memories I
Presentation Lecture
Track Coding for Storage and Memories
Manuscript  Click here to download the manuscript
Virtual Presentation  Click here to watch in the Virtual Symposium
Abstract 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 $\ell$. In the \emph{$(\ell,\delta)$-locally-balanced constraint}, the Hamming weight of every length-$\ell$ subword is bounded between $\ell/2-\delta$ and $\ell/2+\delta$. The \emph{strong-$(\ell,\delta)$-locally-balanced constraint} imposes the locally-balanced constraint for any subword whose length is at least $\ell$. Lastly, the Hamming weight of every length-$\ell$ subword which satisfies the \emph{$(\ell,\delta)$-locally-bounded constraint} is at most $\ell/2-\delta$. It is shown that the capacity of the strong-$(\ell,\delta)$-locally-balanced constraint does not depend on the value of $\ell$ and is identical to the capacity of the \emph{$(2\delta+1)$-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 $2\delta+1$. This value is also a lower bound on the capacity of the $(\ell,\delta)$-locally-balanced constraint, while a corresponding upper bound is given as well. Lastly, it is shown that if $\delta$ is not large enough, namely for $\delta < \sqrt{\ell}/2$, then the capacity of the $(\ell,\delta)$-locally-bounded constraint approaches $1$ as $\ell$ increases.

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2021 IEEE International Symposium on Information Theory

11-16 July 2021 | Melbourne, Victoria, Australia

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