Erasure Coding for Real-Time Streaming

We consider a real-time streaming system where messages are created sequentially at the source, and are encoded for transmission to the receiver over a packet erasure link. Each message must subsequently be decoded at the receiver within a given delay from its creation time. The goal is to construct an erasure correction code that achieves the maximum message size when all messages must be decoded by their respective deadlines under a specified set of erasure patterns (erasure model). We present an explicit intrasession code construction that is asymptotically optimal under erasure models containing a limited number of erasures per coding window, per sliding window, and containing erasure bursts of a limited length.Comment: Extended version of a conference paper in the IEEE International Symposium on Information Theory (ISIT), July 2012. 12 pages, 3 figure

On multiple access random medium access control

In this paper, we develop a new class of medium access control protocol, which allows each user to transmit at different data rates chosen randomly from an appropriately determined set of rates. By using successive interference cancellation, multiple packets can be received simultaneously. In slotted Aloha type Gaussian networks, we show that the achievable total throughput of the proposed protocol is at least a constant fraction of the mac sum rate when the number of transmission rates at each node is equal to the number of users in the network. We also study the case when only a limited number of transmission rates is available at each node. Extension to rate splitting is discussed. Simulation results show that the proposed protocol can achieve a significant throughput gain over the conventional Aloha

Dynamic algorithms for multicast with intra-session network coding

The problem of multiple multicast sessions with intra-session network coding in time-varying networks is considered. The network-layer capacity region of input rates that can be stably supported is established. Dynamic algorithms for multicast routing, network coding, power allocation, session scheduling, and rate allocation across correlated sources, which achieve stability for rates within the capacity region, are presented. This work builds on the back-pressure approach introduced by Tassiulas et al., extending it to network coding and correlated sources. In the proposed algorithms, decisions on routing, network coding, and scheduling between different sessions at a node are made locally at each node based on virtual queues for different sinks. For correlated sources, the sinks locally determine and control transmission rates across the sources. The proposed approach yields a completely distributed algorithm for wired networks. In the wireless case, power control among different transmitters is centralized while routing, network coding, and scheduling between different sessions at a given node are distributed

On the Impact of a Single Edge on the Network Coding Capacity

In this paper, we study the effect of a single link on the capacity of a network of error-free bit pipes. More precisely, we study the change in network capacity that results when we remove a single link of capacity $\delta$. In a recent result, we proved that if all the sources are directly available to a single super-source node, then removing a link of capacity $\delta$ cannot change the capacity region of the network by more than $\delta$ in each dimension. In this paper, we extend this result to the case of multi-source, multi-sink networks for some special network topologies.Comment: Originally presented at ITA 2011 in San Diego, CA. The arXiv version contains an updated proof of Theorem

Statistical Pruning for Near Maximum Likelihood Detection of MIMO Systems

We show a statistical pruning approach for maximum likelihood (ML) detection of multiple-input multiple-output (MIMO) systems. We present a general pruning strategy for sphere decoder (SD), which can also be applied to any tree search algorithms. Our pruning rules are effective especially for the case when SD has high complexity. Three specific pruning rules are given and discussed. From analyzing the union bound on the symbol error probability, we show that the diversity order of the deterministic pruning is only one by fixing the pruning probability. By choosing different pruning probability distribution functions, the statistical pruning can achieve arbitrary diversity orders and SNR gains. Our statistical pruning strategy thus achieves a flexible trade-off between complexity and performance

An information-theoretic view of network management

We present an information-theoretic framework for network management for recovery from nonergodic link failures. Building on recent work in the field of network coding, we describe the input-output relations of network nodes in terms of network codes. This very general concept of network behavior as a code provides a way to quantify essential management information as that needed to switch among different codes (behaviors) for different failure scenarios. We compare two types of recovery schemes, receiver-based and network-wide, and consider two formulations for quantifying network management. The first is a centralized formulation where network behavior is described by an overall code determining the behavior of every node, and the management requirement is taken as the logarithm of the number of such codes that the network may switch among. For this formulation, we give bounds, many of which are tight, on management requirements for various network connection problems in terms of basic parameters such as the number of source processes and the number of links in a minimum source-receiver cut. Our results include a lower bound for arbitrary connections and an upper bound for multitransmitter multicast connections, for linear receiver-based and network-wide recovery from all single link failures. The second is a node-based formulation where the management requirement is taken as the sum over all nodes of the logarithm of the number of different behaviors for each node. We show that the minimum node-based requirement for failures of links adjacent to a single receiver is achieved with receiver-based schemes

Network coding with periodic recomputation for minimum energy multicasting in mobile ad-hoc networks

We consider the problem of minimum-energy multicast using network coding in mobile ad hoc networks (MANETs). The optimal solution can be obtained by solving a linear program every time slot, but it leads to high computational complexity. In this paper, we consider a low-complexity approach, network coding with periodic recomputation, which recomputes an approximate solution at fixed time intervals, and uses this solution during each time interval. As the network topology changes slowly, we derive a theoretical bound on the performance gap between our suboptimal solution and the optimal solution. For complexity analysis, we assume that interior-point method is used to solve a linear program at the first time slot of each interval. Moreover, we can use the suboptimal solution in the preceding interval as a good initial solution of the linear program at each fixed interval. Based on this interior-point method with a warm start strategy, we obtain a bound on complexity. Finally, we consider an example network scenario and minimize the complexity subject to the condition that our solution achieves a given optimality gap

Memoryless Relay Strategies for Two-Way Relay Channels: Performance Analysis and Optimization

We consider relaying strategies for two-way relay channels, where two terminals transmits simultaneously to each other with the help of relays. A memoryless system is considered, where the signal transmitted by a relay depends only on its last received signal. For binary antipodal signaling, we analyze and optimize the performance of existing amplify and forward (AF) and absolute (abs) decode and forward (ADF) for two- way AWGN relay channels. A new abs-based AF (AAF) scheme is proposed, which has better performance than AF. In low SNR, AAF performs even better than ADF. Furthermore, a novel estimate and forward (EF) strategy is proposed which performs better than ADF. More importantly, we optimize the relay strategy within the class of abs-based strategies via functional analysis, which minimizes the average probability of error over all possible relay functions. The optimized function is shown to be a Lambert's W function parameterized on the noise power and the transmission energy. The optimized function behaves like AAF in low SNR and like ADF in high SNR, resp., where EF behaves like the optimized function over the whole SNR range