As parallelism becomes critically important in the semiconductor technology, high-performance computing, and cloud applications, parallel network systems will increasingly follow suit. Today, parallelism is an essential architectural feature of 40 100 400 Gigabit Ethernet standards, whereby high speed Ethernet systems are equipped with multiple parallel network interfaces. This creates new network topology abstractions and new technology requirements: instead of a single high capacity network link, multiple Ethernet end-points and interfaces need to be considered together with multiple links in form of discrete parallel paths. This new paradigm is enabling implementations of various new features to improve overall system performance. In this paper, we analyze the performance of parallel network systems with network coding. In particular, by using random LNC (RLNC), - a code without the need for decoding, we can make use of the fact that we have codes that are both distributed (removing the need for coordination or optimization of resources) and composable (without the need to exchange code information), leading to a fully stateless operation. We propose a novel theoretical modeling framework, including derivation of the upper and lower bounds as well as an expected value of the differential delay of parallel paths, and the resulting queue size at the receiver. The results show a great promise of network system parallelism in combination with RLNC: with a proper set of design parameters, the differential delay and the buffer size at the Ethernet receiver can be reduced significantly, while the cross-layer design and routing can be greatly simplified.
Previous work on linear network coding focused in general on improving network throughput and reliability. However, significant body of work in the last decade (e.g., @cite_24 @cite_32 @cite_3 @cite_23 @cite_11 ) addressed with network coding the end-to-end delays improvement in delay-constrained networks in broadcast and unicast scenarios. In @cite_24 , for instance, the delay performance of network coding was studied and compared it to scheduling methods. Lucani et. al, in @cite_7 tailored coding and feedback to reduce the expected delay. Paper @cite_4 studied the problem of minimizing the mean completion delay for instantly decodable network coding. In @cite_28 @cite_11 authors showed that network coding can outperform optimal routing in single unicast setting. More recent works, like @cite_25 , presented a streaming code that uses forward error correction to reduce in-order delivery delay over multiple parallel wireless networks. However, none of these works address delay in parallel network systems.
@cite_4 @cite_7 @cite_28 @cite_32 @cite_3 @cite_24 @cite_23 @cite_25 @cite_11
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This paper considers network communications under a hard timeliness constraint , where a source node streams perishable information to a destination node over a directed acyclic graph subject to a hard delay constraint. Transmission along any edge incurs unit delay, and it is required that every information bit generated at the source at the beginning of time @math to be received and recovered by the destination at the end of time @math , where @math is the maximum allowed end-to-end delay. We study the corresponding delay-constrained unicast capacity problem. This paper presents the first example showing that network coding (NC) can achieve strictly higher delay-constrained throughput than routing even for the single unicast setting and the NC gain can be arbitrarily close to 2 in some instances. This is in sharp contrast to the delay-unconstrained ( @math ) single-unicast case where the classic min-cut max-flow theorem implies that coding cannot improve throughput over routing. Motivated by the above findings, a series of investigation on the delay-constrained capacity problem is also made, including: 1) an equivalent multiple-unicast representation based on a time-expanded graph approach; 2) a new delay-constrained capacity upper bound and its connections to the existing routing-based results [ 2011]; 3) an example showing that the penalty of using random linear NC can be unbounded; and 4) a counter example of the tree-packing Edmonds’ theorem in the new delay-constrained setting. Built upon the time-expanded graph approach, we also discuss how our results can be readily extended to cyclic networks. Overall, our results suggest that delay-constrained communication is fundamentally different from the well-understood delay-unconstrained one and call for investigation participation. In this paper, we consider the problem of minimizing the completion delay for instantly decodable network coding (IDNC) in wireless multicast and broadcast scenarios. We are interested in this class of network coding due to its numerous benefits, such as low decoding delay, low coding and decoding complexities, and simple receiver requirements. We first extend the IDNC graph, which represents all feasible IDNC coding opportunities, to efficiently operate in both multicast and broadcast scenarios. We then formulate the minimum completion delay problem for IDNC as a stochastic shortest path (SSP) problem. Although finding the optimal policy using SSP is intractable, we use this formulation to draw the theoretical guidelines for the policies that can minimize the completion delay in IDNC. Based on these guidelines, we design a maximum weight clique selection algorithm, which can efficiently reduce the IDNC completion delay in polynomial time. We also design a quadratic-time heuristic clique selection algorithm, which can operate in real-time applications. Simulation results show that our proposed algorithms significantly reduce the IDNC completion delay compared to the random and maximum-rate algorithms, and almost achieve the global optimal completion delay performance over all network codes in broadcast scenarios. A recent approach, COPE, for improving the throughput of unicast traffic in wireless multi-hop networks exploits the broadcast nature of the wireless medium through opportunistic network coding. In this paper, we analyze throughput improvements obtained by COPE-type network coding in wireless networks from a theoretical perspective. We make two key contributions. First, we obtain a theoretical formulation for computing the throughput of network coding on any wireless network topology and any pattern of concurrent unicast traffic sessions. Second, we advocate that routing be made aware of network coding opportunities rather than, as in COPE, being oblivious to it. More importantly, our work studies the tradeoff between routing flows "close to each other" for utilizing coding opportunities and "away from each other" for avoiding wireless interference. Our theoretical formulation provides a method for computing source-destination routes and utilizing the best coding opportunities from available ones so as to maximize the throughput. We handle scheduling of broadcast transmissions subject to wireless transmit receive diversity and link interference in our optimization framework. Using our formulations, we compare the performance of traditional unicast routing and network coding with coding-oblivious and coding-aware routing on a variety of mesh network topologies, including some derived from contemporary mesh network testbeds. Our evaluations show that a route selection strategy that is aware of network coding opportunities leads to higher end-to-end throughput when compared to coding-oblivious routing strategies. A fundamental understanding of the delay behavior of network coding is key towards its successful application in real-time applications with strict message deadlines. Previous contributions focused mostly on the average decoding delay, which although useful in various scenarios of interest is not sufficient for providing worst-case delay guarantees. To overcome this challenge, we investigate the entire delay distribution of random linear network coding for any field size and arbitrary number of encoded symbols (or generation size). By introducing a Markov chain model we are able to obtain a complete solution for the erasure broadcast channel with two receivers. A comparison with Automatic Repeat reQuest (ARQ) with perfect feedback, round robin scheduling and a class of fountain codes reveals that network coding on GF(24) offers the best delay performance for two receivers. We also conclude that GF(2) induces a heavy tail in the delay distribution, which implies that network coding based on XOR operations although simple to implement bears a relevant cost in terms of worst-case delay. For the case of three receivers, which is mathematically challenging, we propose a brute-force methodology that gives the delay distribution of network coding for small generations and field size up to GF(24).