Bounds for Multiple Packing and List-Decoding Error Exponents

Zhang, Yihan; Vatedka, Shashank

doi:10.48550/arxiv.2107.05161

Cited by 1 publication

(4 citation statements)

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“…X-A2 of this paper can be cast as (rigorous) list size bounds for PPPs. The bounds in [48], [49] provide finite list size bounds for PPPs which subsume our bounds in Sec. X-A2.…”

Section: Prior Work On List Decoding Over the Realsmentioning

confidence: 83%

“…2) Blinvosky [48] later generalized their results on PPP to list-L packing for any constant L P Zě 1. However, the proof therein is problematic and is recently corrected in [49] without affecting the result. PPPs are a natural family of ICs.…”

Section: Prior Work On List Decoding Over the Realsmentioning

confidence: 99%

“…3) Some bounds [50], [51] on the list-L capacity of arbitrary spherical codes are also known. Note that the proof in [50] is problematic and is recently corrected in [49] without affecting the result. 4) In computer science, there have been results [52], [53] on efficient list decoding algorithms for explicit lattices, e.g., Barnes-Wall lattices, Barnes-Sloane lattices, etc.…”

Section: Prior Work On List Decoding Over the Realsmentioning

confidence: 99%

“…5) Recently, the authors of the current paper systematically revisited the list decoding problem over R with constant list sizes. Various upper and lower bounds [49] were derived for this problem.…”

Section: Prior Work On List Decoding Over the Realsmentioning

confidence: 99%

See 3 more Smart Citations

List Decoding Random Euclidean Codes and Infinite Constellations

Zhang

Vatedka

2022

IEEE Trans. Inform. Theory

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We study the list decodability of different ensembles of codes over the real alphabet under the assumption of an omniscient adversary. It is a well-known result that when the source and the adversary have power constraints P and N respectively, the list decoding capacity is equal to 1 2 log P N . Random spherical codes achieve constant list sizes, and the goal of the present paper is to obtain a better understanding of the smallest achievable list size as a function of the gap to capacity. We show a reduction from arbitrary codes to spherical codes, and derive a lower bound on the list size of typical random spherical codes. We also give an upper bound on the list size achievable using nested Construction-A lattices and infinite Construction-A lattices. We then define and study a class of infinite constellations that generalize Construction-A lattices and prove upper and lower bounds for the same. Other goodness properties such as packing goodness and AWGN goodness of infinite constellations are proved along the way. Finally, we consider random lattices sampled from the Haar distribution and show that if a certain conjecture that originates in analytic number theory is true, then the list size grows as a polynomial function of the gap-to-capacity.

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“…X-A2 of this paper can be cast as (rigorous) list size bounds for PPPs. The bounds in [48], [49] provide finite list size bounds for PPPs which subsume our bounds in Sec. X-A2.…”

Section: Prior Work On List Decoding Over the Realsmentioning

confidence: 83%

Section: Prior Work On List Decoding Over the Realsmentioning

confidence: 99%