List-Decoding with Double Samplers

We strengthen the notion of double samplers, first introduced by Dinur and Kaufman [``High dimensional expanders imply agreement expanders,” in Proc. 58th IEEE Symp. on Foundations Comp. Science, IEEE, 2017, pp. 974--985], which are samplers with additional combinatorial properties, whose existence we prove using high-dimensional expanders. The ABNNR code construction [N. Alon et al., Trans. Inform. Theory, 38 (1992), 509--516] achieves large distance starting a base $C$ moderate distance, then amplifying sampler. show that if sampler is part larger sampler, has an efficient list-decoding algorithm. Our algorithm works even not applied to but rather any string. In this case resulting approximate-list-decodable, i.e., output list contains approximation original input. as follows: It uses local voting scheme from it constructs unique games constraint graph. graph expander, so can solve efficiently. These solutions list-decoder. This novel use subroutine decoding procedure, opposed more common situation used for demonstrating hardness results. Double akin pseudorandom objects their utility, they greatly exceed random properties. believe these hold significant potential coding theoretic constructions view work power context.