Sandeep Bhadra

Min-Cost Selfish Multicast With Network Coding

The single-source min-cost multicast problem, which can be framed as a convex optimization problem with the use of network codes and convex increasing edge costs is considered. A decentralized approach to this problem is presented by Lun, Ratnakar for the case where all users cooperate to reach the global minimum. Further, the cost for the scenario where each of the multicast receivers greedily routes its flows is analyzed and the existence of a Nash equilibrium is proved. An allocation rule by which edge cost at each edge is allocated to flows through that edge is presented. We prove that under our pricing rule, the flow cost at user equilibrium is the same as the min-cost. This leads to the construction of a selfish flow-steering algorithm for each receiver, which is also globally optimal. Further, the algorithm is extended for completely distributed flow adaptation at nodes in the network to achieve globally minimal cost in steady state. Analogous results are also presented for the case of multiple multicast sessions

Looking at Large Networks: Coding vs. Queueing

Traditionally, network buffer resources have been used at routers to queue transient packets to prevent packet drops. In contrast, we propose a scheme for large multi-hop networks where intermediate routers have no buffers for queueing transient packets. In the proposed scheme, network storage resources (memory) are used only at source and destination nodes to encode/decode packets using random linear coding over time. Our scheme utilizes the observation that for large networks with many flows through each router, if packet loss occurs in a flow path, it will very likely occur only at only one link in the path. Unfortunately, the location of this congested link varies with time, hence, preventing static buffer allocation strategies from exploiting this observation. We propose network coding as a means of “sharing” memory across links along a flow path. We call this spatial buffer multiplexing – where buffering and coding implemented at the source compensates for packet loss at any downstream bufferless link. In this paper, we consider large spatial multi-hop networks with N nodes and Θ(N) flows, where the number of flows through each link scales as Ω(N) for some α ∈ (0, 1). Using many-sources large deviations analysis, we show that to obtain comparable packet drop probabilities (QoS), spatial buffer multiplexing provides an order-wise buffer gain of Ω(N) per node over traditional queueing.

On Network Coding for Interference Networks

We consider a finite-field model for the wireless broadcast and additive interference network (WBAIN), both in the presence and absence of fading. We show that the single-source unicast capacity (with extension to multicast) of a WBAIN with or without fading can be upper bounded by the capacity of an equivalent broadcast erasure network. We further present a coding strategy for WBAINs with i.i.d. and uniform fading based on random linear coding at each node that achieves a rate differing from the upper bound by no more than O(1/q), where q is the field size. Using these results, we show that channel fading in conjunction with network coding can lead to large gains in the unicast (multicast) capacity as compared to no fading

Optimal capacity planning in stochastic loss networks with time-varying workloads

We consider a capacity planning optimization problem in a general theoretical framework that extends the classical Erlang loss modeland related stochastic loss networks to support time-varying workloads. The time horizon consists of a sequence of coarse time intervals, each of which involves a stochastic loss network under a fixed multi-class workload that can change in a general manner from one interval to the next. The optimization problem consists of determining the capacities for each time interval that maximize a utility function over the entire time horizon, finite or infinite, where rewards gained from servicing customers are offset by penalties associated with deploying capacities in an interval and with changing capacities among intervals. We derive a state-dependent optimal policy within the context of a particular limiting regime of the optimization problem, and we prove this solution to be a symptotically optimal. Then, under fairly mild conditions, we prove that a similar structural property holds for the optimal solution of the original stochastic optimization problem, and we show how the optimal capacities comprising this solution can be efficiently computed.

Communication Through Jamming Over a Slotted ALOHA Channel

This correspondence derives bounds on the jamming capacity of a slotted ALOHA system. A system with n legitimate users, each with a Bernoulli arrival process is considered. Packets are temporarily stored at the corresponding user queues, and a slotted ALOHA strategy is used for packet transmissions over the shared channel. The scenario considered is that of a pair of illegitimate users that jam legitimate transmissions in order to communicate over the slotted ALOHA channel. Jamming leads to binary signaling between the illegitimate users, with packet collisions due to legitimate users treated as (multiplicative) noise in this channel. Further, the queueing dynamics at the legitimate users stochastically couples the jamming strategy used by the illegitimate users and the channel evolution. By considering various independent and identically distributed (i.i.d.) jamming strategies, achievable jamming rates over the slotted ALOHA channel are derived. Further, an upper bound on the jamming capacity over the class of all ergodic jamming policies is derived. These bounds are shown to be tight in the limit where the offered system load approaches unity.

Buffer Asymptotics for Coding Over Networks

Traditionally, network buffer resources have been used at routers to queue transient packets to prevent packet drops. In contrast, we propose a scheme for large multihop networks where intermediate routers have no buffers for queueing transient packets. In the proposed scheme, network storage resources (memory) are used only at source and destination nodes to encode/decode packets using random linear coding over time. Our scheme capitalizes on the common empirical observation that for large networks with many flows through each router, if packet loss occurs in a flow path, it will very likely occur only at only a very few links on the path. Unfortunately, the location of this congested link varies with time, thereby preventing prevailing static buffer allocation strategies from exploiting this observation. We propose source coding over packets at the session layer as a means of “sharing” memory across links along a flow path. We call this spatial buffer multiplexing-where buffering and coding implemented at the source compensates for packet loss at any downstream bufferless link. First, we consider large spatial multihop networks with N nodes (each with finite buffer space for coding/decoding) and Θ(N) flows; the number of flows through each link scales as Ω(Nα) for some α ∈ (0,1). Using many-sources large deviations analysis, we show that to obtain comparable packet drop probabilities (QoS), spatial buffer multiplexing provides an order-wise buffer gain of Ω(Nα) per node over traditional static buffer allocation for queueing. Next we consider the complementary case of a network with a small number of flows through a buffer, but large source buffer. Here, we provide a sufficient condition under which the packet loss probability decreases exponentially in a function that is linear in the size of the input buffer, where the function is required to meet a predetermined negative slope -δ. We express the loss effective bandwidth for coding and compare it against that for queueing.

Demo: Achieving robust sensor networks through close coordination between narrow-band power line and low-power wireless communications

Sensor networks are increasingly available in home and industry automation applications. The use of battery-powered wireless sensor nodes eases network deployment, but the dynamic wireless medium, along with energy and bandwidth constraints, poses a great challenge to achieve a robust sensor network only with these nodes. In this demonstration, we present a hybrid sensor node platform equipped with a narrow-band power line communication (PLC) transceiver and a low power RF transceiver, which closely coordinates the two transceivers to improve robustness of a sensor network. Our platform is composed of the TelosB running Contiki and a PLC module that supports several latest narrow-band PLC standards. In addition, we have extended the COOJA simulator of Contiki to support this hybrid sensor node platform in order to aid protocol designs in the context of large sensor networks.

TCP with feed-forward source coding for wireless downlink networks

It is well-known that TCP connections perform poorly over wireless links due to channel fading. To combat this, techniques have been proposed where channel quality feedback is sent to the source, and the source utilizes coding techniques to adapt to the channel state. However, the round-trip time-scales quite often are mismatched to the channel-change time-scale, thus rendering these techniques to be ineffective in this regime. In this paper, we propose a source coding technique that when combined with a queueing strategy at the wireless router, eliminates the need for channel quality feedback to the source. We show that either in a multi-path environment (e.g., the mobile is multi-homed to different wireless networks) or in the presence of multiple TCP connections sharing the same wireless spectrum (where bandwidth can be opportunistically shared between different mobile users), the proposed scheme enables statistical multiplexing of resources, and thus increases TCP throughput dramatically.