Jay Kumar Sundararajan

Network Coding Meets TCP

We propose a mechanism that incorporates network coding into TCP with only minor changes to the protocol stack, thereby allowing incremental deployment. In our scheme, the source transmits random linear combinations of packets currently in the congestion window. At the heart of our scheme is a new interpretation of ACKs - the sink acknowledges every degree of freedom (i.e., a linear combination that reveals one unit of new information) even if it does not reveal an original packet immediately. Such ACKs enable a TCP-compatible sliding-window approach to network coding. Our scheme has the nice property that packet losses are essentially masked from the congestion control algorithm. Our algorithm therefore reacts to packet drops in a smooth manner, resulting in a novel and effective approach for congestion control over networks involving lossy links such as wireless links. Our scheme also allows intermediate nodes to perform re-encoding of the data packets. Our simulations show that our algorithm, with or without re-encoding inside the network, achieves much higher throughput compared to TCP over lossy wireless links. We also establish the soundness and fairness properties of our algorithm. Finally, we present queuing analysis for the case of intermediate node re-encoding.

Network Coding Meets TCP: Theory and Implementation

The theory of network coding promises significant benefits in network performance, especially in lossy networks and in multicast and multipath scenarios. To realize these benefits in practice, we need to understand how coding across packets interacts with the acknowledgment (ACK)-based flow control mechanism that forms a central part of todays Internet protocols such as transmission control protocol (TCP). Current approaches such as rateless codes and batch-based coding are not compatible with TCPs retransmission and sliding-window mechanisms. In this paper, we propose a new mechanism called TCP/NC that incorporates network coding into TCP with only minor changes to the protocol stack, thereby allowing incremental deployment. In our scheme, the source transmits random linear combinations of packets currently in the congestion window. At the heart of our scheme is a new interpretation of ACKs-the sink acknowledges every degree of freedom (i.e., a linear combination that reveals one unit of new information) even if it does not reveal an original packet immediately. Thus, our new TCP ACK rule takes into account the network coding operations in the lower layer and enables a TCP-compatible sliding-window approach to network coding. Coding essentially masks losses from the congestion control algorithm and allows TCP/NC to react smoothly to losses, resulting in a novel and effective approach for congestion control over lossy networks such as wireless networks. An important feature of our solution is that it allows intermediate nodes to perform re-encoding of packets, which is known to provide significant throughput gains in lossy networks and multicast scenarios. Simulations show that our scheme, with or without re-encoding inside the network, achieves much higher throughput compared to TCP over lossy wireless links. We present a real-world implementation of this protocol that addresses the practical aspects of incorporating network coding and decoding with TCPs window management mechanism. We work with TCP-Reno, which is a widespread and practical variant of TCP. Our implementation significantly advances the goal of designing a deployable, general, TCP-compatible protocol that provides the benefits of network coding.

Feedback-Based Online Network Coding

Current approaches to the practical implementation of network coding are batch-based, and often do not use feedback, except possibly to signal completion of a file download. In this paper, the various benefits of using feedback in a network coded system are studied. It is shown that network coding can be performed in a completely online manner, without the need for batches or generations, and that such online operation does not affect the throughput. Although these ideas are presented in a single-hop packet erasure broadcast setting, they naturally extend to more general lossy networks, which employ network coding in the presence of feedback. The impact of feedback on sender-side queue size and receiver-side decoding delay is studied in an asymptotic sense as the traffic load approaches capacity. Different notions of decoding delay are considered, including an order-sensitive notion, which assumes that packets are useful only when delivered in order. Strategies for adaptive coding based on feedback are presented. Our scheme achieves throughput optimality and asymptotically optimal sender queue size and is conjectured to achieve asymptotically optimal in-order delivery delay for any number of receivers. This paper may be viewed as a natural extension of Automatic Repeat reQuest to coded networks.

Online network coding for optimal throughput and delay - the three-receiver case

For a packet erasure broadcast channel with three receivers, we propose a new coding algorithm that makes use of feedback to dynamically adapt the code. Our algorithm is throughput optimal, and we conjecture that it also achieves an asymptotically optimal average decoding delay at the receivers. We consider heavy traffic asymptotics, where the load factor rho approaches 1 from below with either the arrival rate (lambda) or the channel parameter (mu) being fixed at a number less than 1. We verify through simulations that our algorithm achieves an asymptotically optimal decoding delay of O (1/1-rho).

A feedback-based adaptive broadcast coding scheme for reducing in-order delivery delay

We propose a new feedback-based adaptive coding scheme for a packet erasure broadcast channel. The main performance metric of interest is the delay. We consider two types of delay - decoding delay and delivery delay. Decoding delay is the time difference between the instant when the packet is decoded at an arbitrary receiver and the instant when it arrived at the sender. Delivery delay also includes the period when a decoded packet waits in a resequencing buffer at the receiver until all previous packets have also been decoded. This notion of delay is motivated by applications that accept packets only in order. Our coding scheme has the innovation guarantee property and is hence throughput optimal. It also allows efficient queue management. It uses the simple strategy of mixing only the oldest undecoded packet of each receiver, and therefore extends to any number of receivers. We conjecture that this scheme achieves the asymptotically optimal delivery (and hence decoding) delay. The asymptotic behavior is studied in the limit as the load factor of the system approaches capacity. This conjecture is verified through simulations.

Collision Helps - Algebraic Collision Recovery for Wireless Erasure Networks

Current medium access control mechanisms are based on collision avoidance and collided packets are discarded. The recent work on ZigZag decoding departs from this approach by recovering the original packets from multiple collisions. In this paper, we present an algebraic representation of collisions which allows us to view each collision as a linear combination of the original packets. The transmitted, colliding packets may themselves be a coded version of the original packets. We propose a new acknowledgment (ACK) mechanism for collisions based on the idea that if a set of packets collide, the receiver can afford to ACK exactly one of them and still decode all the packets eventually. We analytically compare delay performance of such collision recovery schemes with other collision avoidance approaches in the context of a single hop wireless erasure network. From the delay perspective, our scheme, without any coordination, outperforms not only ALOHA-type random access mechanisms, but also centralized scheduling.

Extending the Birkhoff-von Neumann switching strategy for multicast - On the use of optical splitting in switches

The Birkhoff-von Neumann (BVN) strategy for single-stage input-queued crossbar switches does not support multicast, as it considers only permutation-based switch configurations. This paper extends the BVN strategy to multicast switching, where an input can simultaneously transmit to multiple outputs. Knowledge of the average rates of flows is used to compute an offline schedule. We begin by considering a system in which the fanout of each flow is split in a predecided manner. We call this static splitting (as opposed to dynamic splitting where no such constraint is imposed), and we study the rate region of the switch under this restriction. We provide a graph-theoretic formulation of the rate region.

Comparison of schemes for streaming multicast in cellular networks with relays

Multicasting is emerging as an important application in both cellular networks and wireless sensor networks. We consider several schemes for enhancing throughput and coverage for streaming multicast sessions by allowing intermediate nodes to relay information from the source. The schemes exploit the broadcast nature of the wireless medium, and techniques such as received signal combining and network coding to enhance performance while guaranteeing that a constant streaming delay is experienced by every user. The performance metric used for comparison is the throughput achieved at a given area coverage probability. Specifically, we study techniques such as decode-and-forward, amplify-and-forward, and pipelining and compare their performances through simulations in the context of a cellular network with relays and show that significant performance benefits are obtained through such schemes

A modification to RED AQM for CIOQ switches

In very large networks with heavy traffic, congestion control plays an important role in network resource management. One approach to this is the active queue management (AQM) algorithms. Many AQM algorithms have been proposed and analyzed but they mainly focus on single queued links. Recognizing the fact that input queued switches are limited in throughput and output queued switches require a large speedup factor, we direct our attention to combined input and output queued (CIOQ) switches. We propose a simple modification to the RED AQM algorithm in order to account for the presence of both input and output queues in the switch. Specifically we use the weighted sum of input and output queue lengths as the congestion measure instead of just the output queue length. Simulations show that with such a simple modification, the average backlog in the switch is significantly reduced in the low speedup region as compared to RED without this modification. Unlike the traditional dynamic of having the loss rate grow with the length of the queue, simulations show that for a loss rate in the modified RED slightly larger than that in RED, the output queue length in modified RED is tremendously reduced. The weighting factor used in the computation of the congestion measure provides a means to balance the reduction in the average backlog on the one hand, and the increase in the loss rate on the other hand. Finally, simulations show that the improvement gained in terms of the queue length does not compromise in any way the utilization of the switch as compared to RED and Droptail.

Acknowledgement design for collision-recovery-enabled wireless erasure networks

Current medium access control mechanisms are based on collision avoidance and collided packets are discarded. The recent work on ZigZag decoding departs from this approach by recovering the original packets from multiple collisions. In this paper, we view each collision as a linear combination of the original packets at the senders. The transmitted, colliding packets may themselves be a coded version of the original packets.