High-Probability List-Recovery, and Applications to Heavy Hitters

An error correcting code C: Σ^k → Σⁿ is efficiently list-recoverable from input list size ℓ if for any sets L₁,..., L_n ⊆ Σ of size at most ℓ, one can efficiently recover the list L = {x ∈ Σ^k : ∀j ∈ [n], C(x)_j ∈ L_j}. While list-recovery has been well-studied in error correcting codes, all known constructions with “efficient” algorithms are not efficient in the parameter ℓ. In this work, motivated by applications in algorithm design and pseudorandomness, we study list-recovery with the goal of obtaining a good dependence on ℓ. We make a step towards this goal by obtaining it in the weaker case where we allow a randomized encoding map and a small failure probability, and where the input lists are derived from unions of codewords. As an application of our construction, we give a data structure for the heavy hitters problem in the strict turnstile model that, for some parameter regimes, obtains stronger guarantees than known constructions.