# Technical Program

## Paper Detail

 Paper ID M.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.