Worst-case probability strings require e^{Ω(√n)} traces to distinguish under deletions, while random probability strings are recoverable to ℓ1 error ε with poly(n,1/ε) traces.
Coded trace reconstruction
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A Generalized Trace Reconstruction Problem: Recovering a String of Probabilities
Worst-case probability strings require e^{Ω(√n)} traces to distinguish under deletions, while random probability strings are recoverable to ℓ1 error ε with poly(n,1/ε) traces.