Distributed minimum cost multicasting with lossless source coding and network coding

In this paper, we consider minimum cost lossless source coding for multiple multicast sessions. Each session comprises a set of correlated sources whose information is demanded by a set of sink nodes. We propose a distributed end-to-end algorithm which operates over given multicast trees, and a back-pressure algorithm which optimizes routing and coding over the whole network. Unlike other existing algorithms, the source rates need not be centrally coordinated; the sinks control transmission rates across the sources. With random network coding, the proposed approach yields completely distributed and optimal algorithms for intra-session network coding. We prove the convergence of our proposed algorithms. Some practical considerations are also discussed. Experimental results are provided to complement our theoretical analysis

Heuristics for Network Coding in Wireless Networks

Multicast is a central challenge for emerging multi-hop wireless architectures such as wireless mesh networks, because of its substantial cost in terms of bandwidth. In this report, we study one specific case of multicast: broadcasting, sending data from one source to all nodes, in a multi-hop wireless network. The broadcast we focus on is based on network coding, a promising avenue for reducing cost; previous work of ours showed that the performance of network coding with simple heuristics is asymptotically optimal: each transmission is beneficial to nearly every receiver. This is for homogenous and large networks of the plan. But for small, sparse or for inhomogeneous networks, some additional heuristics are required. This report proposes such additional new heuristics (for selecting rates) for broadcasting with network coding. Our heuristics are intended to use only simple local topology information. We detail the logic of the heuristics, and with experimental results, we illustrate the behavior of the heuristics, and demonstrate their excellent performance

Minimum-cost multicast over coded packet networks

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

Computation Over Gaussian Networks With Orthogonal Components

Function computation of arbitrarily correlated discrete sources over Gaussian networks with orthogonal components is studied. Two classes of functions are considered: the arithmetic sum function and the type function. The arithmetic sum function in this paper is defined as a set of multiple weighted arithmetic sums, which includes averaging of the sources and estimating each of the sources as special cases. The type or frequency histogram function counts the number of occurrences of each argument, which yields many important statistics such as mean, variance, maximum, minimum, median, and so on. The proposed computation coding first abstracts Gaussian networks into the corresponding modulo sum multiple-access channels via nested lattice codes and linear network coding and then computes the desired function by using linear Slepian-Wolf source coding. For orthogonal Gaussian networks (with no broadcast and multiple-access components), the computation capacity is characterized for a class of networks. For Gaussian networks with multiple-access components (but no broadcast), an approximate computation capacity is characterized for a class of networks.Comment: 30 pages, 12 figures, submitted to IEEE Transactions on Information Theor

Novel approaches to performance evaluation and benchmarking for energy-efficient multicast: empirical study of coded packet wireless networks

With the advancement of communication networks, a great number of multicast applications such as multimedia, video and audio communications have emerged. As a result, energy efficient multicast in wireless networks is becoming increasingly important in the field of Information and Communications Technology (ICT). According to the study by Gartner and Environmental Protection Agency (EPA) report presented to United State Congress in 2007,energy consumption of ICT nodes accounts for 3% of the worldwide energy supply and is responsible for 2% of the global Carbon dioxide (CO2) emission. However, several initiatives are being put in place to reduce the energy consumption of the ICT sector in general. A review of related literature reveals that existing approaches to energy efficient multicast are largely evaluated using a single metric and while the single metric is appropriate for effective performance, it is unsuitable for measuring efficiency adequately. This thesis studied existing coded packet methods for energy efficiency in ad hoc wireless networks and investigates efficiency frontier, which is the expected minimum energy within the minimum energy multicast framework. The energy efficiency performance was based on effective evaluation and there was no way an inefficient network could reach a level of being an efficiency frontier. Hence, this work looked at the position of how true efficiency evaluation is obtained when the entire network under examination attains their efficiency frontiers using ratios of weighted outputs to weighted inputs with multiple variables. To address these challenges and assist network operators when formulating their network policies and performing network administrations, this thesis proposed novel approaches that are based on Data Envelopment Analysis (DEA) methodology to appropriately evaluate the efficiency of multicast energy and further minimizes energy transmission in ad hoc wireless networks without affecting the overall network performance. The DEA, which was used to study the relative efficiency and productivity of systems in Economic and Operational Research disciplines, is a non-parametric method that relies on linear programming technique for optimization of discrete units of observation called the decision making units (DMUs)

Block-Diagonal and LT Codes for Distributed Computing With Straggling Servers

We propose two coded schemes for the distributed computing problem of multiplying a matrix by a set of vectors. The first scheme is based on partitioning the matrix into submatrices and applying maximum distance separable (MDS) codes to each submatrix. For this scheme, we prove that up to a given number of partitions the communication load and the computational delay (not including the encoding and decoding delay) are identical to those of the scheme recently proposed by Li et al., based on a single, long MDS code. However, due to the use of shorter MDS codes, our scheme yields a significantly lower overall computational delay when the delay incurred by encoding and decoding is also considered. We further propose a second coded scheme based on Luby Transform (LT) codes under inactivation decoding. Interestingly, LT codes may reduce the delay over the partitioned scheme at the expense of an increased communication load. We also consider distributed computing under a deadline and show numerically that the proposed schemes outperform other schemes in the literature, with the LT code-based scheme yielding the best performance for the scenarios considered.Comment: To appear in IEEE Transactions on Communication