Interactive Coding with Small Memory and Improved Rate
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2024
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866910564671815680 |
|---|---|
| author | Fathollahi, Dorsa Haeupler, Bernhard Resch, Nicolas Wootters, Mary |
| author_facet | Fathollahi, Dorsa Haeupler, Bernhard Resch, Nicolas Wootters, Mary |
| contents | In this work, we study two-party interactive coding for adversarial noise, when both parties have limited memory. We show how to convert any adaptive protocol $Π$ into a protocol $Π'$ that is robust to an $ε$-fraction of adversarial corruptions, not too much longer than $Π$, and which uses small space. More precisely, if $Π$ requires space $\log(s)$ and has $|Π|$ rounds of communication, then $Π'$ requires $O_ε(\log s \log |Π|)$ memory, and has $$|Π'| = |Π|\cdot\left( 1 + O\left( \sqrt{ ε\log \log 1/ε} \right)\right)$$ rounds of communication. The above matches the best known communication rate, even for protocols with no space restrictions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_06541 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Interactive Coding with Small Memory and Improved Rate Fathollahi, Dorsa Haeupler, Bernhard Resch, Nicolas Wootters, Mary Information Theory In this work, we study two-party interactive coding for adversarial noise, when both parties have limited memory. We show how to convert any adaptive protocol $Π$ into a protocol $Π'$ that is robust to an $ε$-fraction of adversarial corruptions, not too much longer than $Π$, and which uses small space. More precisely, if $Π$ requires space $\log(s)$ and has $|Π|$ rounds of communication, then $Π'$ requires $O_ε(\log s \log |Π|)$ memory, and has $$|Π'| = |Π|\cdot\left( 1 + O\left( \sqrt{ ε\log \log 1/ε} \right)\right)$$ rounds of communication. The above matches the best known communication rate, even for protocols with no space restrictions. |
| title | Interactive Coding with Small Memory and Improved Rate |
| topic | Information Theory |
| url | https://arxiv.org/abs/2408.06541 |