On Coding for Cooperative Data Exchange

We consider the problem of data exchange by a group of closely-located wireless nodes. In this problem each node holds a set of packets and needs to obtain all the packets held by other nodes. Each of the nodes can broadcast the packets in its possession (or a combination thereof) via a noiseless broadcast channel of capacity one packet per channel use. The goal is to minimize the total number of transmissions needed to satisfy the demands of all the nodes, assuming that they can cooperate with each other and are fully aware of the packet sets available to other nodes. This problem arises in several practical settings, such as peer-to-peer systems and wireless data broadcast. In this paper, we establish upper and lower bounds on the optimal number of transmissions and present an efficient algorithm with provable performance guarantees. The effectiveness of our algorithms is established through numerical simulations.Comment: Appeared in the proceedings of the 2010 IEEE Information Theory Workshop (ITW 2010, Cairo

Throughput and Delay Optimization of Linear Network Coding in Wireless Broadcast

Linear network coding (LNC) is able to achieve the optimal throughput of packet-level wireless broadcast, where a sender wishes to broadcast a set of data packets to a set of receivers within its transmission range through lossy wireless links. But the price is a large delay in the recovery of individual data packets due to network decoding, which may undermine all the benefits of LNC. However, packet decoding delay minimization and its relation to throughput maximization have not been well understood in the network coding literature. Motivated by this fact, in this thesis we present a comprehensive study on the joint optimization of throughput and average packet decoding delay (APDD) for LNC in wireless broadcast. To this end, we reveal the fundamental performance limits of LNC and study the performance of three major classes of LNC techniques, including instantly decodable network coding (IDNC), generation-based LNC, and throughput-optimal LNC (including random linear network coding (RLNC)). Various approaches are taken to accomplish the study, including 1) deriving performance bounds, 2) establishing and modelling optimization problems, 3) studying the hardness of the optimization problems and their approximation, 4) developing new optimal and heuristic techniques that take into account practical concerns such as receiver feedback frequency and computational complexity. Key contributions of this thesis include: - a necessary and sufficient condition for LNC to achieve the optimal throughput of wireless broadcast; - the NP-hardness of APDD minimization; - lower bounds of the expected APDD of LNC under random packet erasures; - the APDD-approximation ratio of throughput-optimal LNC, which has a value of between 4/3 and 2. In particular, the ratio of RLNC is exactly 2; - a novel throughput-optimal, APDD-approximation, and implementation-friendly LNC technique; - an optimal implementation of strict IDNC that is robust to packet erasures; - a novel generation-based LNC technique that generalizes some of the existing LNC techniques and enables tunable throughput-delay tradeoffs

Random network coding‐based optimal scheme for perfect wireless packet retransmission problems

Solving wireless packet retransmission problems (WPRTPs) using network coding (NC) approach is increasingly attracting research efforts. However, existing researches are almost all focused on solutions in Galois field GF(2), and consequently, the solutions found by these schemes are usually less optimal. In this paper, we focus on optimal NC‐based scheme for perfect WPRTPs (P‐WPRTPs) where, with respect to each receiver, a packet is either requested by or already known to it. The number of retransmitted packets in optimal NC‐based solutions to P‐WPRTPs is firstly analyzed and proved. Then, random network coding‐based optimal scheme (RNCOPT) is proposed for P‐WRPTPs. RNCOPT is optimal in the sense that it guarantees to obtain a valid solution with minimum number of packet retransmissions. Furthermore, in RNCOPT, each coding vector is generated using a publicly known pseudorandom function with a randomly selected seed. The seed, instead of the coding vector, is used as decoding information to be retransmitted together with the coded packet. Thus, packet overhead of RNCOPT is reduced further. Extensive simulations show that RNCOPT distinctively outperforms some previous typical schemes for P‐WPRTPs in saving the number of retransmitted packets. Copyright © 2011 John Wiley & Sons, Ltd. This paper studied Perfect Wireless Packet ReTransmission Problems (P‐WPRTPs) where, with respect to each receiver, a packet is either requested by or already known to it. The number of retransmitted packets in optimal NC‐based solutions to P‐WPRTPs was analyzed and proved. Then, random network coding‐based optimal scheme (RNCOPT) is proposed for P‐WPRTPs. RNCOPT is optimal in the sense that it guarantees to obtain a valid solution with minimum number of packet retransmissions.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/97523/1/wcm1122.pd

Design and Analysis of Efficient Index Coding Methods for Future Wireless Communications

This thesis considers the problem of efficient broadcast in a system where a single server transmits a set of messages to a number of users via a noiseless broadcast channel. Each user requests one specific message and may know some of the other messages a priori as its side information. This problem is known as the index coding problem and was first introduced by Birk and Kol [Birk and Kol, 1998], in the context of satellite communications. Exploiting the side information of the receivers along with the coding techniques at the server can reduce the number of transmissions to satisfy all the receivers. The simple model in index coding can establish a useful framework for studying other research areas, including network coding, distributed storage systems, and coded caching. In this thesis, index coding is approached from a new perspective to propose a new scalar linear coding scheme called the update-based maximum column distance (UMCD) coding scheme. In the beginning, the receivers are sorted based on the size of their side information. Then, in each transmission, a linear combination of the messages is designed to instantaneously satisfy one of the receivers with the minimum size of side information. Then, the problem is updated by eliminating all receivers who are able to decode their requested message from the coded messages received so far along with the messages in their side information. This process is repeated until all receivers can successfully decode their requested message. Concrete instances are provided to show that the proposed UMCD coding scheme has a better broadcast performance compared to the most efficient existing coding schemes, including the recursive coding scheme (Arbabjolfaei and Kim, 2014) and the interlinked-cycle cover coding scheme (Thapa et al., 2017). Also in this thesis, the insufficiency of linear coding and the necessity of nonlinear codes for index coding problem are investigated, with two main contributions. First, while the insufficiency of linear coding has been proved for network coding (Dougherty et al., 2005), groupcast index coding (Effros et al., 2015), and asymmetric-rate unicast index coding (Maleki et al., 2014), it remained an open problem for symmetric-rate unicast index coding. In this thesis, we settle this open question by constructing two symmetric-rate unicast index coding instances of sizes 33 and 36 for which optimal linear coding is outperformed by nonlinear codes. Second, while it has been known that the insufficiency of linear coding is due to the dependency of its rate on the field size, this dependency has been illustrated only over fields with characteristic two. In this thesis, we extend this limit to the fields with characteristic three by constructing two index coding instances of size 29. It is shown that while for the first instance, linear coding is optimal only over fields with characteristic three, for the second instance, linear coding over any fields with characteristic three can never be optimal. Finally in this thesis, a new coding scheme called the independent user partition multicast (IUPM) is proposed for the groupcast index coding. It is proved that the proposed IUPM coding scheme includes the two most efficient coding schemes, namely the user partition multicast (Shanmugam et al., 2015) and the packet partition multicast (Tehrani et al., 2012), as special cases. Then, a new polynomial-time algorithm for solving the general groupcast index coding problem is proposed. We show that the proposed heuristic algorithm can outperform the approximation partition multicast coding scheme (Unal and Wagner, 2016) for a class of groupcast index coding instances

Fundamental Limits of Caching in Wireless D2D Networks

We consider a wireless Device-to-Device (D2D) network where communication is restricted to be single-hop. Users make arbitrary requests from a finite library of files and have pre-cached information on their devices, subject to a per-node storage capacity constraint. A similar problem has already been considered in an ``infrastructure'' setting, where all users receive a common multicast (coded) message from a single omniscient server (e.g., a base station having all the files in the library) through a shared bottleneck link. In this work, we consider a D2D ``infrastructure-less'' version of the problem. We propose a caching strategy based on deterministic assignment of subpackets of the library files, and a coded delivery strategy where the users send linearly coded messages to each other in order to collectively satisfy their demands. We also consider a random caching strategy, which is more suitable to a fully decentralized implementation. Under certain conditions, both approaches can achieve the information theoretic outer bound within a constant multiplicative factor. In our previous work, we showed that a caching D2D wireless network with one-hop communication, random caching, and uncoded delivery, achieves the same throughput scaling law of the infrastructure-based coded multicasting scheme, in the regime of large number of users and files in the library. This shows that the spatial reuse gain of the D2D network is order-equivalent to the coded multicasting gain of single base station transmission. It is therefore natural to ask whether these two gains are cumulative, i.e.,if a D2D network with both local communication (spatial reuse) and coded multicasting can provide an improved scaling law. Somewhat counterintuitively, we show that these gains do not cumulate (in terms of throughput scaling law).Comment: 45 pages, 5 figures, Submitted to IEEE Transactions on Information Theory, This is the extended version of the conference (ITW) paper arXiv:1304.585