Estimating Minimum Sum-rate for Cooperative Data Exchange

This paper considers how to accurately estimate the minimum sum-rate so as to reduce the complexity of solving cooperative data exchange (CDE) problems. The CDE system contains a number of geographically close clients who send packets to help the others recover an entire packet set. The minimum sum-rate is the minimum value of total number of transmissions that achieves universal recovery (the situation when all the clients recover the whole packet set). Based on a necessary and sufficient condition for a supermodular base polyhedron to be nonempty, we show that the minimum sum-rate for a CDE system can be determined by a maximization over all possible partitions of the client set. Due to the high complexity of solving this maximization problem, we propose a deterministic algorithm to approximate a lower bound on the minimum sum-rate. We show by experiments that this lower bound is much tighter than those lower bounds derived in the existing literature. We also show that the deterministic algorithm prevents from repetitively running the existing algorithms for solving CDE problems so that the overall complexity can be reduced accordingly.Comment: 6 pages, 6 figure

Iterative Merging Algorithm for Cooperative Data Exchange

We consider the problem of finding the minimum sum-rate strategy in cooperative data exchange systems that do not allow packet-splitting (NPS-CDE). In an NPS-CDE system, there are a number of geographically close cooperative clients who send packets to help the others recover a packet set. A minimum sum-rate strategy is the strategy that achieves universal recovery (the situation when all the clients recover the whole packet set) with the the minimal sum-rate (the total number of transmissions). We propose an iterative merging (IM) algorithm that recursively merges client sets based on a lower estimate of the minimum sum-rate and updates to the value of the minimum sum-rate. We also show that a minimum sum-rate strategy can be learned by allocating rates for the local recovery in each merged client set in the IM algorithm. We run an experiment to show that the complexity of the IM algorithm is lower than that of the existing deterministic algorithm when the number of clients is lower than $94$.Comment: 9 pages, 3 figure

A Practical Approach for Successive Omniscience

The system that we study in this paper contains a set of users that observe a discrete memoryless multiple source and communicate via noise-free channels with the aim of attaining omniscience, the state that all users recover the entire multiple source. We adopt the concept of successive omniscience (SO), i.e., letting the local omniscience in some user subset be attained before the global omniscience in the entire system, and consider the problem of how to efficiently attain omniscience in a successive manner. Based on the existing results on SO, we propose a CompSetSO algorithm for determining a complimentary set, a user subset in which the local omniscience can be attained first without increasing the sum-rate, the total number of communications, for the global omniscience. We also derive a sufficient condition for a user subset to be complimentary so that running the CompSetSO algorithm only requires a lower bound, instead of the exact value, of the minimum sum-rate for attaining global omniscience. The CompSetSO algorithm returns a complimentary user subset in polynomial time. We show by example how to recursively apply the CompSetSO algorithm so that the global omniscience can be attained by multi-stages of SO

New expression for the functional transformation of the vector Cramér-Rao lower bound

Assume that it is desired to estimate α = f(θ), where f(·) is an r-dimensional function. This paper derives the general expression for the functional transformation of the vector Cramér-Rao lower bound (CRLB). The derived bound is a tight lower bound on the estimation of uncoupled parameters, i.e., parameters that can be estimated separately. Unlike previous results in the literature, this new expression is not dependent on the inverse of the Fisher's information matrix (FIM) of the untransformed parameters, θ. Thus, it can be applied to scenarios where the FIM for θ is ill-conditioned or singular. Finally, as an application, the derived transformation is applied to determine the exact CRLB for estimation of channel parameters in amplify-and-forward relaying networks.This research was supported under Australian Research Council’s Discovery Projects funding scheme (project number DP110102548)