We present a distributed random linear network coding approach for transmission and compression of information in general multisource multicast networks. Network nodes independently and randomly select linear mappings from inputs onto output links over some field. We show that this achieves capacity with probability exponentially approaching 1 with the code length. We also demonstrate that random linear coding performs compression when necessary in a network, generalizing error exponents for linear Slepian-Wolf coding in a natural way. Benefits of this approach are decentralized operation and robustness to network changes or link failures. We show that this approach can take advantage of redundant network capacity for improved success probability and robustness. We illustrate some potential advantages of random linear network coding over routing in two examples of practical scenarios: distributed network operation and networks with dynamically varying connections. Our derivation of these results also yields a new bound on required field size for centralized network coding on general multicast networks

/pdf/a-random-linear-network-coding-approach-to-multicast-4j4cdceo1m.pdf

A Random Linear Network Coding Approach to Multicast

This paper proposes COPE, a new architecture for wireless mesh networks. In addition to forwarding packets, routers mix (i.e., code) packets from different sources to increase the information content of each transmission. We show that intelligently mixing packets increases network throughput. Our design is rooted in the theory of network coding. Prior work on network coding is mainly theoretical and focuses on multicast traffic. This paper aims to bridge theory with practice; it addresses the common case of unicast traffic, dynamic and potentially bursty flows, and practical issues facing the integration of network coding in the current network stack. We evaluate our design on a 20-node wireless network, and discuss the results of the first testbed deployment of wireless network coding. The results show that using COPE at the forwarding layer, without modifying routing and higher layers, increases network throughput. The gains vary from a few percent to several folds depending on the traffic pattern, congestion level, and transport protocol.

/pdf/xors-in-the-air-practical-wireless-network-coding-17k31b3st4.pdf

XORs in the air: practical wireless network coding

Network protocols in layered architectures have historically been obtained on an ad hoc basis, and many of the recent cross-layer designs are also conducted through piecemeal approaches. Network protocol stacks may instead be holistically analyzed and systematically designed as distributed solutions to some global optimization problems. This paper presents a survey of the recent efforts towards a systematic understanding of layering as optimization decomposition, where the overall communication network is modeled by a generalized network utility maximization problem, each layer corresponds to a decomposed subproblem, and the interfaces among layers are quantified as functions of the optimization variables coordinating the subproblems. There can be many alternative decompositions, leading to a choice of different layering architectures. This paper surveys the current status of horizontal decomposition into distributed computation, and vertical decomposition into functional modules such as congestion control, routing, scheduling, random access, power control, and channel coding. Key messages and methods arising from many recent works are summarized, and open issues discussed. Through case studies, it is illustrated how layering as Optimization Decomposition provides a common language to think about modularization in the face of complex, networked interactions, a unifying, top-down approach to design protocol stacks, and a mathematical theory of network architectures

/pdf/layering-as-optimization-decomposition-a-mathematical-theory-3t9xhz4cfy.pdf

Layering as Optimization Decomposition: A Mathematical Theory of Network Architectures

| Network protocols in layered architectures have historically been obtained on an ad hoc basis, and many of the recent cross-layer designs are also conducted through piecemeal approaches. Network protocol stacks may instead be holistically analyzed and systematically designed as distributed solutions to some global optimization problems. This paper presents a survey of the recent efforts towards a systematic understanding of "layering" as "optimization decomposition," where the overall communication network is modeled by a generalized network utility maximization problem, each layer corresponds to a decomposed subproblem, and the interfaces among layers are quantified as functions of the optimization variables coordinating the subproblems. There can be many alternative decompositions, leading to a choice of different layering architectures. This paper surveys the current status of horizontal decomposition into distributed computation, and vertical decomposition into functional modules such as congestion control, routing, scheduling, random access, power control, and channel coding. Key messages and methods arising from many recent works are summarized, and open issues discussed. Through case studies, it is illustrated how "Layering as Optimization Decomposition" provides a common language to think about modularization in the face of complex, networked interactions, a unifying, top-down approach to design protocol stacks, and a mathematical theory of network architectures.

Layering as optimization decomposition: A mathematical theory of network architectures : There are various ways that network functionalities can be allocated to different layers and to different network elements, some being more desirable than others. The intellectual goal of the research surveyed by this article is to provide a theoretical foundation for these architectural decisions in networking

This paper proposes COPE, a new architecture for wireless mesh networks. In addition to forwarding packets, routers mix (i.e., code) packets from different sources to increase the information content of each transmission. We show that intelligently mixing packets increases network throughput. Our design is rooted in the theory of network coding. Prior work on network coding is mainly theoretical and focuses on multicast traffic. This paper aims to bridge theory with practice; it addresses the common case of unicast traffic, dynamic and potentially bursty flows, and practical issues facing the integration of network coding in the current network stack. We evaluate our design on a 20-node wireless network, and discuss the results of the first testbed deployment of wireless network coding. The results show that COPE largely increases network throughput. The gains vary from a few percent to several folds depending on the traffic pattern, congestion level, and transport protocol.

/pdf/xors-in-the-air-practical-wireless-network-coding-39etlzp2kc.pdf

We consider the problem of establishing minimum-cost multicast connections over coded packet networks, i.e., packet networks where the contents of outgoing packets are arbitrary, causal functions of the contents of received packets. We consider both wireline and wireless packet networks as well as both static multicast (where membership of the multicast group remains constant for the duration of the connection) and dynamic multicast (where membership of the multicast group changes in time, with nodes joining and leaving the group). For static multicast, we reduce the problem to a polynomial-time solvable optimization problem, and we present decentralized algorithms for solving it. These algorithms, when coupled with existing decentralized schemes for constructing network codes, yield a fully decentralized approach for achieving minimum-cost multicast. By contrast, establishing minimum-cost static multicast connections over routed packet networks is a very difficult problem even using centralized computation, except in the special cases of unicast and broadcast connections. For dynamic multicast, we reduce the problem to a dynamic programming problem and apply the theory of dynamic programming to suggest how it may be solved.

/pdf/minimum-cost-multicast-over-coded-packet-networks-38leh89nep.pdf

Minimum-cost multicast over coded packet networks

We present decentralized algorithms that compute minimum-cost subgraphs for establishing multicast connections in networks that use coding. These algorithms, coupled with existing decentralized schemes for constructing network codes, constitute a fully decentralized approach for achieving minimum-cost multicast. Our approach is in sharp contrast to the prevailing approach based on approximation algorithms for the directed Steiner tree problem, which is suboptimal and generally assumes centralized computation with full network knowledge. We also give extensions beyond the basic problem of fixed-rate multicast in networks with directed point-to-point links, and consider the case of elastic rate demand as well as the problem of minimum-energy multicast in wireless networks.

Achieving minimum-cost multicast: a decentralized approach based on network coding

In an unreliable packet network setting, we study the performance gains of optimal transmission strategies in the presence and absence of coding capability at the transmitter, where performance is measured in delay and throughput. Although our results apply to a large class of coding strategies including maximum-distance separable (MDS) and Digital Fountain codes, we use random network codes in our discussions because these codes have a greater applicability for complex network topologies. To that end, after introducing a key setting in which performance analysis and comparison can be carried out, we provide closed-form as well as asymptotic expressions for the delay performance with and without network coding. We show that the network coding capability can lead to arbitrarily better delay performance as the system parameters scale when compared to traditional transmission strategies without coding. We further develop a joint scheduling and random-access scheme to extend our results to general wireless network topologies.

/pdf/on-the-delay-and-throughput-gains-of-coding-in-unreliable-2nyk9gqt22.pdf

On the Delay and Throughput Gains of Coding in Unreliable Networks

We study the scaling law governing the delay gains of network coding as compared to traditional transmission strategies in unreliable wireless networks. We distinguish between two types of traffic, namely elastic and inelastic, where the elasticity of a flow is based on the delay constraints associated with it. This novel formulation is useful in that it allows for the modeling of real-time traffic more accurately. Considering the limited availability of feedback in such systems, we focus on strategies with minimal acknowledgement requirements. Under both traffic types, we provide an extensive analysis of the gains of network coding as compared to traditional transmission strategies in a single-hop setting, and show that the gains are significant in general and can be considerably large in some cases. We further provide a method for realizing these gains in multi-hop networks with general topologies using the analysis of the single hop scenario.

http://www2.ece.ohio-state.edu/~eryilmaz/papers/NC_Scaling07.pdf

On the Scaling Law of Network Coding Gains in Wireless Networks

BACKGROUND Early detection of rejection in kidney transplant recipients holds the promise to improve clinical outcomes. Development and implementation of more accurate, noninvasive methods to detect allograft rejection remain an ongoing challenge. The limitations of existing allograft surveillance methods present an opportunity for donor-derived cell-free DNA (dd-cfDNA), which can accurately and rapidly differentiate patients with allograft rejection from patients with stable organ function. METHODS This study evaluated the analytical performance of a massively multiplexed polymerase chain reaction assay that targets 13 962 single-nucleotide polymorphisms, characterized and validated using 66 unique samples with 1064 replicates, including cell line-derived reference samples, plasma-derived mixtures, and transplant patient samples. The dd-cfDNA fraction was quantified in both related and unrelated donor-recipient pairs. RESULTS The dd-cfDNA assay showed a limit of blank of 0.11%, a limit of detection and limit of quantitation of 0.15% for unrelated donors, and limit of blank of 0.23%, a limit of detection and limit of quantitation of 0.29% for related donors. All other metrics (linearity, accuracy, and precision) were observed to be equivalent between unrelated and related donors. The measurement precision of coefficient of variation was 1.8% (repeatability, 0.6% dd-cfDNA) and was <5% for all the different reproducibility measures. CONCLUSIONS This study validates the performance of a single-nucleotide polymorphism-based massively multiplexed polymerase chain reaction assay to detect the dd-cfDNA fraction with improved precision over currently available tests, regardless of donor-recipient relationships.

Analytical Validation of a Single-nucleotide Polymorphism-based Donor-derived Cell-free DNA Assay for Detecting Rejection in Kidney Transplant Patients.

Ebad Ahmed

Papers

Minimum-cost multicast over coded packet networks

Achieving minimum-cost multicast: a decentralized approach based on network coding

On the Delay and Throughput Gains of Coding in Unreliable Networks

On the Scaling Law of Network Coding Gains in Wireless Networks

Analytical Validation of a Single-nucleotide Polymorphism-based Donor-derived Cell-free DNA Assay for Detecting Rejection in Kidney Transplant Patients.