Rigorous Lower Bound on the Kirsch–Drinea Correction

Establish a rigorous lower bound for the nonnegative correction to the Drinea–Mitzenmacher jigsaw rate in the binary deletion channel that is estimated by simulation in the Kirsch–Drinea approach.

Background

The Drinea–Mitzenmacher jigsaw functional omits a nonnegative correction arising when the mutual information rate is decomposed into the jigsaw rate plus additional uncertainty reduction. Kirsch and Drinea introduced this correction but estimated it using Monte Carlo simulation.

The paper notes that surveys record no rigorous lower bound for this correction. Consequently, the provable content of the simulation-based approach coincides with the older jigsaw lower bound, leaving rigorous exploitation of the correction unresolved.