All reports by Author Ray Li:

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TR21-079
| 9th June 2021
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Venkatesan Guruswami, Xiaoyu He, Ray Li#### The zero-rate threshold for adversarial bit-deletions is less than 1/2

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TR20-168
| 11th November 2020
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Zeyu Guo, Ray Li, Chong Shangguan, Itzhak Tamo, Mary Wootters#### Improved List-Decodability of Reedâ€“Solomon Codes via Tree Packings

Venkatesan Guruswami, Xiaoyu He, Ray Li

We prove that there exists an absolute constant $\delta>0$ such any binary code $C\subset\{0,1\}^N$ tolerating $(1/2-\delta)N$ adversarial deletions must satisfy $|C|\le 2^{\poly\log N}$ and thus have rate asymptotically approaching $0$. This is the first constant fraction improvement over the trivial bound that codes tolerating $N/2$ adversarial deletions must have rate ... more >>>

Zeyu Guo, Ray Li, Chong Shangguan, Itzhak Tamo, Mary Wootters

This paper shows that there exist Reed--Solomon (RS) codes, over large finite fields, that are combinatorially list-decodable well beyond the Johnson radius, in fact almost achieving list-decoding capacity. In particular, we show that for any $\epsilon\in (0,1]$ there exist RS codes with rate $\Omega(\frac{\epsilon}{\log(1/\epsilon)+1})$ that are list-decodable from radius of ... more >>>