Cooperative Data Exchange with Unreliable Clients

Consider a set of clients in a broadcast network, each of which holds a subset of packets in the ground set X. In the (coded) cooperative data exchange problem, the clients need to recover all packets in X by exchanging coded packets over a lossless broadcast channel. Several previous works analyzed this problem under the assumption that each client initially holds a random subset of packets in X. In this paper we consider a generalization of this problem for settings in which an unknown (but of a certain size) subset of clients are unreliable and their packet transmissions are subject to arbitrary erasures. For the special case of one unreliable client, we derive a closed-form expression for the minimum number of transmissions required for each reliable client to obtain all packets held by other reliable clients (with probability approaching 1 as the number of packets tends to infinity). Furthermore, for the cases with more than one unreliable client, we provide an approximation solution in which the number of transmissions per packet is within an arbitrarily small additive factor from the value of the optimal solution.Comment: 8 pages; in Proc. 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton 2015

Successive Local and Successive Global Omniscience

This paper considers two generalizations of the cooperative data exchange problem, referred to as the successive local omniscience (SLO) and the successive global omniscience (SGO). The users are divided into $\ell$ nested sub-groups. Each user initially knows a subset of packets in a ground set $X$ of size $k$, and all users wish to learn all packets in $X$. The users exchange their packets by broadcasting coded or uncoded packets. In SLO or SGO, in the $l$th ($1\leq l\leq \ell$) round of transmissions, the $l$th smallest sub-group of users need to learn all packets they collectively hold or all packets in $X$, respectively. The problem is to find the minimum sum-rate (i.e., the total transmission rate by all users) for each round, subject to minimizing the sum-rate for the previous round. To solve this problem, we use a linear-programming approach. For the cases in which the packets are randomly distributed among users, we construct a system of linear equations whose solution characterizes the minimum sum-rate for each round with high probability as $k$ tends to infinity. Moreover, for the special case of two nested groups, we derive closed-form expressions, which hold with high probability as $k$ tends to infinity, for the minimum sum-rate for each round.Comment: Accepted for publication in Proc. ISIT 201

How Fast Can Dense Codes Achieve the Min-Cut Capacity of Line Networks?

In this paper, we study the coding delay and the average coding delay of random linear network codes (dense codes) over line networks with deterministic regular and Poisson transmission schedules. We consider both lossless networks and networks with Bernoulli losses. The upper bounds derived in this paper, which are in some cases more general, and in some other cases tighter, than the existing bounds, provide a more clear picture of the speed of convergence of dense codes to the min-cut capacity of line networks.Comment: 15 pages, submitted to IEEE ISIT 201