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 Ω(1) that are list-decodable from a 0.707-fraction of insertions. For any τ_I ≥ 0 and τ_D ∈ [0, 1), there exist q-ary codes of rate Ω(1) that are list-decodable from a τ_I-fraction of insertions and τ_I-fraction of deletions, where q depends only on τ_I and τ . We also provide efficient encoding and decoding algorithms for list-decoding from τ_I-fraction of insertions and τ -fraction of deletions for any τ_I ≥ 0 and τ_D ∈ [0, 1). Based on the Johnson-type bound, we derive a Plotkin-type upper bound on the code size in the Levenshtein metric.