Distributed MAC Protocol Supporting Physical-Layer Network Coding

Physical-layer network coding (PNC) is a promising approach for wireless networks. It allows nodes to transmit simultaneously. Due to the difficulties of scheduling simultaneous transmissions, existing works on PNC are based on simplified medium access control (MAC) protocols, which are not applicable to general multi-hop wireless networks, to the best of our knowledge. In this paper, we propose a distributed MAC protocol that supports PNC in multi-hop wireless networks. The proposed MAC protocol is based on the carrier sense multiple access (CSMA) strategy and can be regarded as an extension to the IEEE 802.11 MAC protocol. In the proposed protocol, each node collects information on the queue status of its neighboring nodes. When a node finds that there is an opportunity for some of its neighbors to perform PNC, it notifies its corresponding neighboring nodes and initiates the process of packet exchange using PNC, with the node itself as a relay. During the packet exchange process, the relay also works as a coordinator which coordinates the transmission of source nodes. Meanwhile, the proposed protocol is compatible with conventional network coding and conventional transmission schemes. Simulation results show that the proposed protocol is advantageous in various scenarios of wireless applications.Comment: Final versio

Network Codes for Real-Time Applications

We consider the scenario of broadcasting for real-time applications and loss recovery via instantly decodable network coding. Past work focused on minimizing the completion delay, which is not the right objective for real-time applications that have strict deadlines. In this work, we are interested in finding a code that is instantly decodable by the maximum number of users. First, we prove that this problem is NP-Hard in the general case. Then we consider the practical probabilistic scenario, where users have i.i.d. loss probability and the number of packets is linear or polynomial in the number of users. In this scenario, we provide a polynomial-time (in the number of users) algorithm that finds the optimal coded packet. The proposed algorithm is evaluated using both simulation and real network traces of a real-time Android application. Both results show that the proposed coding scheme significantly outperforms the state-of-the-art baselines: an optimal repetition code and a COPE-like greedy scheme.Comment: ToN 2013 Submission Versio

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

Cooperative Data Exchange based on MDS Codes

The cooperative data exchange problem is studied for the fully connected network. In this problem, each node initially only possesses a subset of the $K$ packets making up the file. Nodes make broadcast transmissions that are received by all other nodes. The goal is for each node to recover the full file. In this paper, we present a polynomial-time deterministic algorithm to compute the optimal (i.e., minimal) number of required broadcast transmissions and to determine the precise transmissions to be made by the nodes. A particular feature of our approach is that {\it each} of the $K-d$ transmissions is a linear combination of {\it exactly} $d+1$ packets, and we show how to optimally choose the value of $d.$ We also show how the coefficients of these linear combinations can be chosen by leveraging a connection to Maximum Distance Separable (MDS) codes. Moreover, we show that our method can be used to solve cooperative data exchange problems with weighted cost as well as the so-called successive local omniscience problem.Comment: 21 pages, 1 figur

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

Coded Cooperative Data Exchange for a Secret Key

We consider a coded cooperative data exchange problem with the goal of generating a secret key. Specifically, we investigate the number of public transmissions required for a set of clients to agree on a secret key with probability one, subject to the constraint that it remains private from an eavesdropper. Although the problems are closely related, we prove that secret key generation with fewest number of linear transmissions is NP-hard, while it is known that the analogous problem in traditional cooperative data exchange can be solved in polynomial time. In doing this, we completely characterize the best possible performance of linear coding schemes, and also prove that linear codes can be strictly suboptimal. Finally, we extend the single-key results to characterize the minimum number of public transmissions required to generate a desired integer number of statistically independent secret keys.Comment: Full version of a paper that appeared at ISIT 2014. 19 pages, 2 figure