On the List Decodability of Insertions and Deletions

In this work, we study the problem of list decoding of insertions and deletions. We present a Johnson-type upper bound on the maximum list size. The bound is meaningful only when insertions occur. Our bound implies that there are binary codes of rate \Omega (1) that are list-decodable from a 0.707-fraction of insertions. For any \tau _{\mathsf {I}} \geq 0 and \tau _{\mathsf {D}} \in [0,1) , there exist q -ary codes of rate \Omega (1) that are list-decodable from a \tau _{\mathsf {I}} -fraction of insertions and \tau _{\mathsf {D}} -fraction of deletions, where q depends only on \tau _{\mathsf {I}} and \tau _{\mathsf {D}} . We also provide efficient encoding and decoding algorithms for list-decoding from \tau _{\mathsf {I}} -fraction of insertions and \tau _{\mathsf {D}} -fraction of deletions for any \tau _{\mathsf {I}} \geq 0 and \tau _{\mathsf {D}} \in [0,1) . Based on the Johnson-type bound, we derive a Plotkin-type upper bound on the code size in the Levenshtein metric.