English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The input-constrained erasure channel with feedback is considered, where thebinary input sequence contains no consecutive ones, i.e., it satisfies the$(1,\infty)$-RLL constraint. We derive the capacity for this setting, which canbe expressed as $C_{\epsilon}=\max_{0 \leq p \leq\frac{1}{2}}\frac{H_{b}(p)}{p+\frac{1}{1-\epsilon}}$, where $\epsilon$ is theerasure probability and $ H_{b}(\cdot)$ is the binary entropy function.Moreover, we prove that a-priori knowledge of the erasure at the encoder doesnot increase the feedback capacity. The feedback capacity was calculated usingan equivalent dynamic programming (DP) formulation with an optimalaverage-reward that is equal to the capacity. Furthermore, we obtained anoptimal encoding procedure from the solution of the DP, leading to acapacity-achieving, zero-error coding scheme for our setting. DP is thus shownto be a tool not only for solving optimization problems such as capacitycalculation, but also for constructing optimal coding schemes. The derivedcapacity expression also serves as the only non-trivial upper bound known onthe capacity of the input-constrained erasure channel without feedback, aproblem that is still open.

The Feedback Capacity of the $(1,\infty)$-RLL Input-Constrained Erasure Channel