On the communication cost of determining an approximate nearest lattice point

Bollauf, Maiara F.; Vaishampayan, Vinay A.; Costa, Sueli I. R.

doi:10.1109/isit.2017.8006847

Cited by 8 publications

(9 citation statements)

References 20 publications

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“…partitions R n into two classes f −1 (0) = {X : X s < a} and its complement f −1 (1). We assume here that X i are independent, identically distributed (iid) random variables, uniformly distributed on the unit interval [0, 1).…”

Section: Problem Setupmentioning

confidence: 99%

Classification in a Large Network

Vaishampayan

2019

2019 IEEE International Symposium on Information Theory (ISIT)

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We construct and analyze the communication cost of protocols (interactive and one-way) for classifying X = (X1, X2, . . . , Xn) ∈ [0, 1) n ⊂ R n , in a network with n ≥ 2 nodes, with Xi known only at node i. The classifier takes the form n i=1 hiXi ≷ a, with weights hi ∈ {−1, +1}. The interactive protocol (a zero-error protocol) exchanges a variable number of messages depending on the input X and its sum rate is directly proportional to its mean stopping time. An exact analysis, as well as an approximation of the mean stopping time is presented and shows that it depends on γ = α + (1/2 − β), where α = a/n and β = m/n, with m being the number of positive weights. In particular, the mean stopping time grows logarithmically in n when γ = 0, and is bounded in n otherwise. Comparisons show that the sum rate of the interactive protocol is smaller than that of the one-way protocol when the error probability for the oneway protocol is small, with the reverse being true when the error probability is large. Comparisons of the interactive protocol are also made with lower bounds on the sum rate.

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Section: Problem Setupmentioning

confidence: 99%

Classification in a Large Network

Vaishampayan

2019

2019 IEEE International Symposium on Information Theory (ISIT)

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“…In a companion paper [5] we have developed upper bounds for the communication complexity of constructing a specific rectangular partition for a given lattice along with a closed form expression for the error probability P e . The partition is referred to as a Babai partition and is an approximation to the Voronoi partition for a given lattice.…”

Section: )mentioning

confidence: 99%

“…However, when the lattice is scaled by α (i.e. the generator matrix for the lattice is αV) and det V = 1 it is easy to show that the Stage-I rate satisfies [5]…”

Section: A Analysis Of Rate In Stage-imentioning

confidence: 99%

On the Interactive Communication Cost of the Distributed Nearest Lattice Point Problem

Vaishampayan,

Bollauf

2018

Preprint

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We consider the problem of distributed computation of the nearest lattice point for a two dimensional lattice. An interactive two-party model of communication is considered. Algorithms with bounded, as well as unbounded, number of rounds of communication are considered. For the algorithm with a bounded number of rounds, expressions are derived for the error probability as a function of the total number of communicated bits. We observe that the error exponent depends on the lattice. With an infinite number of allowed communication rounds, the average cost of achieving zero error probability is shown to be finite.

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“…We consider a two-stage approach for determining λ(x). In Stage-I, [3], a point λ np (x) (defined next) is determined, using the nearest plane algorithm [1], and assuming an interactive model. We refer to λ np (x) as the Babai point.…”

Section: Previous Workmentioning

confidence: 99%

“…In a companion paper [3] we have developed upper bounds for the communication complexity of constructing a specific rectangular partition for a given lattice along with a closed form expression for the error probability P e . The partition is referred to as a Babai partition and is an approximation to the Voronoi partition for a given lattice.…”

Section: Introductionmentioning

confidence: 99%

Communication cost of transforming a nearest plane partition to the Voronoi partition

Vaishampayan

Bollauf

2017

2017 IEEE International Symposium on Information Theory (ISIT)

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Abstract-We consider the problem of distributed computation of the nearest lattice point for a two dimensional lattice. An interactive model of communication is considered. We address the problem of reconfiguring a specific rectangular partition, a nearest plane, or Babai, partition, into the Voronoi partition. Expressions are derived for the error probability as a function of the total number of communicated bits. With an infinite number of allowed communication rounds, the average cost of achieving zero error probability is shown to be finite. For the interactive model, with a single round of communication, expressions are obtained for the error probability as a function of the bits exchanged. We observe that the error exponent depends on the lattice.

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On the communication cost of determining an approximate nearest lattice point

Cited by 8 publications

References 20 publications

Classification in a Large Network

Classification in a Large Network

On the Interactive Communication Cost of the Distributed Nearest Lattice Point Problem

Communication cost of transforming a nearest plane partition to the Voronoi partition

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