Optimal Immediately-Decodable Inter-session Network Coding (IDNC) Schemes for Two Unicast Sessions with Hard Deadline Constraints

In this paper, we study inter-session network coding for sending two unicast sessions over an unreliable wireless channel. Each unicast session transmits a stored video file, whose packets have hard sequential deadline constraints. We first characterize the capacity region (with inter-session network coding) for the transmission rates of the two unicast sessions under heterogeneous channel conditions and heterogeneous deadline constraints. We then develop immediately-decodable network coding (IDNC) schemes for controlling packet transmissions for the unicast sessions subject to hard deadline constraints. In contrast to our prior work that focuses on a single multicast session with homogeneous channel conditions and deadline constraints, the design and performance analysis of the IDNC scheme is much more complicated for unicast-sessions because of the asymmetry due to heterogeneous channel conditions and heterogeneous deadlines. Nonetheless, we establish the optimality of the proposed IDNC scheme when the file sizes are sufficiently large

Dynamic Rate Adaptation for Improved Throughput and Delay in Wireless Network Coded Broadcast

In this paper we provide theoretical and simulation-based study of the delivery delay performance of a number of existing throughput optimal coding schemes and use the results to design a new dynamic rate adaptation scheme that achieves improved overall throughput-delay performance. Under a baseline rate control scheme, the receivers' delay performance is examined. Based on their Markov states, the knowledge difference between the sender and receiver, three distinct methods for packet delivery are identified: zero state, leader state and coefficient-based delivery. We provide analyses of each of these and show that, in many cases, zero state delivery alone presents a tractable approximation of the expected packet delivery behaviour. Interestingly, while coefficient-based delivery has so far been treated as a secondary effect in the literature, we find that the choice of coefficients is extremely important in determining the delay, and a well chosen encoding scheme can, in fact, contribute a significant improvement to the delivery delay. Based on our delivery delay model, we develop a dynamic rate adaptation scheme which uses performance prediction models to determine the sender transmission rate. Surprisingly, taking this approach leads us to the simple conclusion that the sender should regulate its addition rate based on the total number of undelivered packets stored at the receivers. We show that despite its simplicity, our proposed dynamic rate adaptation scheme results in noticeably improved throughput-delay performance over existing schemes in the literature.Comment: 14 pages, 15 figure

Effective Delay Control in Online Network Coding

Motivated by streaming applications with stringent delay constraints, we consider the design of online network coding algorithms with timely delivery guarantees. Assuming that the sender is providing the same data to multiple receivers over independent packet erasure channels, we focus on the case of perfect feedback and heterogeneous erasure probabilities. Based on a general analytical framework for evaluating the decoding delay, we show that existing ARQ schemes fail to ensure that receivers with weak channels are able to recover from packet losses within reasonable time. To overcome this problem, we re-define the encoding rules in order to break the chains of linear combinations that cannot be decoded after one of the packets is lost. Our results show that sending uncoded packets at key times ensures that all the receivers are able to meet specific delay requirements with very high probability.Comment: 9 pages, IEEE Infocom 200

Coding in 802.11 WLANs

Forward error correction (FEC) coding is widely used in communication systems to correct transmis- sion errors. In IEEE 802.11a/g transmitters, convolutional codes are used for FEC at the physical (PHY) layer. As is typical in wireless systems, only a limited choice of pre-speci¯ed coding rates is supported. These are implemented in hardware and thus di±cult to change, and the coding rates are selected with point to point operation in mind. This thesis is concerned with using FEC coding in 802.11 WLANs in more interesting ways that are better aligned with application requirements. For example, coding to support multicast tra±c rather than simple point to point tra±c; coding that is cognisant of the multiuser nature of the wireless channel; and coding which takes account of delay requirements as well as losses. We consider layering additional coding on top of the existing 802.11 PHY layer coding, and investigate the tradeo® between higher layer coding and PHY layer modulation and FEC coding as well as MAC layer scheduling. Firstly we consider the joint multicast performance of higher-layer fountain coding concatenated with 802.11a/g OFDM PHY modulation/coding. A study on the optimal choice of PHY rates with and without fountain coding is carried out for standard 802.11 WLANs. We ¯nd that, in contrast to studies in cellular networks, in 802.11a/g WLANs the PHY rate that optimizes uncoded multicast performance is also close to optimal for fountain-coded multicast tra±c. This indicates that in 802.11a/g WLANs cross-layer rate control for higher-layer fountain coding concatenated with physical layer modulation and FEC would bring few bene¯ts. Secondly, using experimental measurements taken in an outdoor environment, we model the chan- nel provided by outdoor 802.11 links as a hybrid binary symmetric/packet erasure channel. This hybrid channel o®ers capacity increases of more than 100% compared to a conventional packet erasure channel (PEC) over a wide range of RSSIs. Based upon the established channel model, we further consider the potential performance gains of adopting a binary symmetric channel (BSC) paradigm for multi-destination aggregations in 802.11 WLANs. We consider two BSC-based higher-layer coding approaches, i.e. superposition coding and a simpler time-sharing coding, for multi-destination aggre- gated packets. The performance results for both unicast and multicast tra±c, taking account of MAC layer overheads, demonstrate that increases in network throughput of more than 100% are possible over a wide range of channel conditions, and that the simpler time-sharing approach yields most of these gains and have minor loss of performance. Finally, we consider the proportional fair allocation of high-layer coding rates and airtimes in 802.11 WLANs, taking link losses and delay constraints into account. We ¯nd that a layered approach of separating MAC scheduling and higher-layer coding rate selection is optimal. The proportional fair coding rate and airtime allocation (i) assigns equal total airtime (i.e. airtime including both successful and failed transmissions) to every station in a WLAN, (ii) the station airtimes sum to unity (ensuring operation at the rate region boundary), and (iii) the optimal coding rate is selected to maximise goodput (treating packets decoded after the delay deadline as losses)

Adaptive Network Coding for Scheduling Real-time Traffic with Hard Deadlines

We study adaptive network coding (NC) for scheduling real-time traffic over a single-hop wireless network. To meet the hard deadlines of real-time traffic, it is critical to strike a balance between maximizing the throughput and minimizing the risk that the entire block of coded packets may not be decodable by the deadline. Thus motivated, we explore adaptive NC, where the block size is adapted based on the remaining time to the deadline, by casting this sequential block size adaptation problem as a finite-horizon Markov decision process. One interesting finding is that the optimal block size and its corresponding action space monotonically decrease as the deadline approaches, and the optimal block size is bounded by the "greedy" block size. These unique structures make it possible to narrow down the search space of dynamic programming, building on which we develop a monotonicity-based backward induction algorithm (MBIA) that can solve for the optimal block size in polynomial time. Since channel erasure probabilities would be time-varying in a mobile network, we further develop a joint real-time scheduling and channel learning scheme with adaptive NC that can adapt to channel dynamics. We also generalize the analysis to multiple flows with hard deadlines and long-term delivery ratio constraints, devise a low-complexity online scheduling algorithm integrated with the MBIA, and then establish its asymptotical throughput-optimality. In addition to analysis and simulation results, we perform high fidelity wireless emulation tests with real radio transmissions to demonstrate the feasibility of the MBIA in finding the optimal block size in real time.Comment: 11 pages, 13 figure

Network Coding for Delay Constrained Wireless Systems with Feedback

Rousseau Pierre. Une base de colonne découverte dans l'église de Saint-Germain-des-Prés à Paris. In: Bulletin de la Société Nationale des Antiquaires de France, 1975, 1977. pp. 47-48