Coding against deletions in oblivious and online models
Venkatesan Guruswami, Ray Li

TL;DR
This paper investigates deletion error-correcting codes in different models, showing that codes can correct nearly all deletions in oblivious models and establishing equivalences between thresholds in adversarial and online deletion scenarios.
Contribution
It introduces the zero-rate thresholds for oblivious and online deletion models, proving that codes can handle nearly all deletions in the oblivious case and relating thresholds between models.
Findings
Codes exist with positive rate for any fraction less than 1 in oblivious deletions.
The zero-rate threshold for oblivious deletions is exactly 1.
Thresholds for adversarial and online deletion models are equivalent at 1/2.
Abstract
We consider binary error correcting codes when errors are deletions. A basic challenge concerning deletion codes is determining , the zero-rate threshold of adversarial deletions, defined to be the supremum of all for which there exists a code family with rate bounded away from 0 capable of correcting a fraction of adversarial deletions. A recent construction of deletion-correcting codes [Bukh et al 17] shows that , and the trivial upper bound, , is the best known. Perhaps surprisingly, we do not know whether or not . In this work, to gain further insight into deletion codes, we explore two related error models: oblivious deletions and online deletions, which are in between random and adversarial deletions in power. In the oblivious model, the channel can inflict an arbitrary pattern of …
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