An Improved Bound on the Fraction of Correctable Deletions

Boris Bukh, Venkatesan Guruswami, Johan Hastad
2017 IEEE Transactions on Information Theory  
We consider codes over fixed alphabets against worst-case symbol deletions. For any fixed k 2, we construct a family of codes over alphabet of size k with positive rate, which allow efficient recovery from a worst-case deletion fraction approaching 1 − 2 k+1 . In particular, for binary codes, we are able to recover a fraction of deletions approaching 1/3. Previously, even non-constructively the largest deletion fraction known to be correctable with positive rate was 1 − Θ(1/ √ k), and around
more » ... 7 for the binary case. Our result pins down the largest fraction of correctable deletions for k-ary codes as 1 − Θ(1/k), since 1 − 1/k is an upper bound even for the simpler model of erasures where the locations of the missing symbols are known. Closing the gap between 1/3 and 1/2 for the limit of worst-case deletions correctable by binary codes remains a tantalizing open question.
doi:10.1109/tit.2016.2621044 fatcat:q32omapj5zdg7fyx2ep7iewvsy