Linear Network Coding for Two-Unicast-ZZ Networks: A Commutative Algebraic Perspective and Fundamental Limits

We consider a two-unicast-$Z$ network over a directed acyclic graph of unit capacitated edges; the two-unicast-$Z$ network is a special case of two-unicast networks where one of the destinations has apriori side information of the unwanted (interfering) message. In this paper, we settle open questions on the limits of network coding for two-unicast-$Z$ networks by showing that the generalized network sharing bound is not tight, vector linear codes outperform scalar linear codes, and non-linear codes outperform linear codes in general. We also develop a commutative algebraic approach to deriving linear network coding achievability results, and demonstrate our approach by providing an alternate proof to the previous results of C. Wang et. al., I. Wang et. al. and Shenvi et. al. regarding feasibility of rate $(1,1)$ in the network.Comment: A short version of this paper is published in the Proceedings of The IEEE International Symposium on Information Theory (ISIT), June 201

A Linear Network Code Construction for General Integer Connections Based on the Constraint Satisfaction Problem

The problem of finding network codes for general connections is inherently difficult in capacity constrained networks. Resource minimization for general connections with network coding is further complicated. Existing methods for identifying solutions mainly rely on highly restricted classes of network codes, and are almost all centralized. In this paper, we introduce linear network mixing coefficients for code constructions of general connections that generalize random linear network coding (RLNC) for multicast connections. For such code constructions, we pose the problem of cost minimization for the subgraph involved in the coding solution and relate this minimization to a path-based Constraint Satisfaction Problem (CSP) and an edge-based CSP. While CSPs are NP-complete in general, we present a path-based probabilistic distributed algorithm and an edge-based probabilistic distributed algorithm with almost sure convergence in finite time by applying Communication Free Learning (CFL). Our approach allows fairly general coding across flows, guarantees no greater cost than routing, and shows a possible distributed implementation. Numerical results illustrate the performance improvement of our approach over existing methods.Comment: submitted to TON (conference version published at IEEE GLOBECOM 2015

Source Broadcasting to the Masses: Separation has a Bounded Loss

This work discusses the source broadcasting problem, i.e. transmitting a source to many receivers via a broadcast channel. The optimal rate-distortion region for this problem is unknown. The separation approach divides the problem into two complementary problems: source successive refinement and broadcast channel transmission. We provide bounds on the loss incorporated by applying time-sharing and separation in source broadcasting. If the broadcast channel is degraded, it turns out that separation-based time-sharing achieves at least a factor of the joint source-channel optimal rate, and this factor has a positive limit even if the number of receivers increases to infinity. For the AWGN broadcast channel a better bound is introduced, implying that all achievable joint source-channel schemes have a rate within one bit of the separation-based achievable rate region for two receivers, or within $\log_2 T$ bits for $T$ receivers

Studies on efficient spectrum sharing in coexisting wireless networks.

Wireless communication is facing serious challenges worldwide: the severe spectrum shortage along with the explosive increase of the wireless communication demands. Moreover, different communication networks may coexist in the same geographical area. By allowing multiple communication networks cooperatively or opportunistically sharing the same frequency will potentially enhance the spectrum efficiency. This dissertation aims to investigate important spectrum sharing schemes for coexisting networks. For coexisting networks operating in interweave cognitive radio mode, most existing works focus on the secondary network’s spectrum sensing and accessing schemes. However, the primary network can be selfish and tends to use up all the frequency resource. In this dissertation, a novel optimization scheme is proposed to let primary network maximally release unnecessary frequency resource for secondary networks. The optimization problems are formulated for both uplink and downlink orthogonal frequency-division multiple access (OFDMA)-based primary networks, and near optimal algorithms are proposed as well. For coexisting networks in the underlay cognitive radio mode, this work focuses on the resource allocation in distributed secondary networks as long as the primary network’s rate constraint can be met. Global optimal multicarrier discrete distributed (MCDD) algorithm and suboptimal Gibbs sampler based Lagrangian algorithm (GSLA) are proposed to solve the problem distributively. Regarding to the dirty paper coding (DPC)-based system where multiple networks share the common transmitter, this dissertation focuses on its fundamental performance analysis from information theoretic point of view. Time division multiple access (TDMA) as an orthogonal frequency sharing scheme is also investigated for comparison purpose. Specifically, the delay sensitive quality of service (QoS) requirements are incorporated by considering effective capacity in fast fading and outage capacity in slow fading. The performance metrics in low signal to noise ratio (SNR) regime and high SNR regime are obtained in closed forms followed by the detailed performance analysis

Scalable on-demand streaming of stored complex multimedia

Previous research has developed a number of efficient protocols for streaming popular multimedia files on-demand to potentially large numbers of concurrent clients. These protocols can achieve server bandwidth usage that grows much slower than linearly with the file request rate, and with the inverse of client start-up delay. This hesis makes the following three main contributions to the design and performance evaluation of such protocols. The first contribution is an investigation of the network bandwidth requirements for scalable on-demand streaming. The results suggest that the minimum required network bandwidth for scalable on-demand streaming typically scales as K/ln(K) as the number of client sites K increases for fixed request rate per client site, and as ln(N/(ND+1)) as the total file request rate N increases or client start-up delay D decreases, for a fixed number of sites. Multicast delivery trees configured to minimize network bandwidth usage rather than latency are found to only modestly reduce the minimum required network bandwidth. Furthermore, it is possible to achieve close to the minimum possible network and server bandwidth usage simultaneously with practical scalable delivery protocols. Second, the thesis addresses the problem of scalable on-demand streaming of a more complex type of media than is typically considered, namely variable bit rate (VBR) media. A lower bound on the minimum required server bandwidth for scalable on-demand streaming of VBR media is derived. The lower bound analysis motivates the design of a new immediate service protocol termed VBR bandwidth skimming (VBRBS) that uses constant bit rate streaming, when sufficient client storage space is available, yet fruitfully exploits the knowledge of a VBR profile. Finally, the thesis proposes non-linear media containing parallel sequences of data frames, among which clients can dynamically select at designated branch points, and investigates the design and performance issues in scalable on-demand streaming of such media. Lower bounds on the minimum required server bandwidth for various non-linear media scalable on-demand streaming approaches are derived, practical non-linear media scalable delivery protocols are developed, and, as a proof-of-concept, a simple scalable delivery protocol is implemented in a non-linear media streaming prototype system