CRBcast: A Collaborative Rateless Scheme for Reliable and Energy-Efficient Broadcasting in Wireless Sensor/Actuator Networks Nazanin Rahnavard, Badri N. Vellambi R., and Faramarz Fekri Problem Analysis of Probabilistic Relaying CRBcast Protocol Phase I Encoding data packets by rateless coding at the source node Broadcasting k encoded packets with a light-weight PBcast (small p) At the end of Phase I we have two types of nodes: Theorem: G(N,r,p) is a connected dominating graph if and only if p>pth, where pth is given by Objective Broadcasting in multihop wireless networks Energy-Efficient Reliable Scalable Low Complexity: Requires no topology knowledge Motivation Updating software in already deployed sensor/actuator networks Broadcasting route query packets in reactive routing schemes Key revoking of compromised keys Some Related Work Flooding [Obraczka99], Probabilistic Broadcast [Tseng99], Counter-Based Scheme [Tseng99], GARUDA [Park04], Dominating Set Based Scheme [Stojmenovic02], … Our Approach Employing an efficient erasure coding (Rateless Coding) to recover for losses in conjunction with a probabilistic relaying G(N,r) : Corresponding graph (N: # of nodes, r : Trans. range) G(N,r,p) : Subgraph G induced by potential relay nodes (each node is a relay node with probability p) A: area of deployment, (N): Any slowly growing function of N such that Complete nodes: Nodes received at least k distinct packets and can decode and retrieve original packets Incomplete nodes: Nodes did not receive enough packets to decode Phase II (based on collaboration of complete and incomplete nodes) Complete nodes Advertise (ADV) their completeness to their neighbors Incomplete nodes Request (REQ) the number of required packets Complete nodes send maximum number of needed packets by generating new packets based on the retrieved original data (decoding and re-encoding) One packet 2000 packets About 7000 transmissions per packet For 99% reliability Reliability decreases a lot P = 0.7 for 99% reliability Almost all nodes receive the packet REQ, j packets ADV DATA, max(i,j) packets pth =0.43 REQ, i packets Reliability (fraction of nodes that receive all packets) versus forwarding probability p in PBcast Number of transmissions per packet versus forwarding probability p in PBcast N = 10000, r = 25, A = 1000x1000 (i) (ii) (iii) Our Proposal: CRBcast Simulation Results Motivation An easy, energy-efficient, and scalable broadcasting scheme Providing reliability with little penalty Low complexity Require no optimization and no topology information N=10000, k=2000 packets, =1.03 popt w pgiant Optimal Solution Nodes with only Relaying Capability Minimum Connected Dominating Set (MCDS) Finding MCDS is NP hard! Nodes with Coding and Relaying Capabilities Network Coding [Ahlswede00] [Lun, Medard, Effros 04], … Polynomial complexity for a given directed graph, however: q has to be very large to have innovative packets Gaussian elimination for decoding: complexity O(k3) (k: number of packets to be broadcasted) Overhead (klog2q) for sending the global encoding vector Uneven load balancing Non optimal for dynamic networks and unknown channels Our Approach Use an efficient erasure coding (rateless coding) to recover for losses CRBcast (collaborative rateless broadcast) has two phases: Phase I : A light-weight PBcast (small p) on rateless coded packets Phase II : A final recovery scheme based on an Advertisement and Request scheme # of transmission at Phase I is an increasing function of p # of transmission at Phase II is a decreasing function of p Popt (optimal forwarding probability) minimizes # of transmissions Rateless Codes Channel parameters are different and unknown A source can generate potentially infinite supply of encoding packets from the original data Any receiver collects as many packets as it needs to complete the decoding Receivers are at one hop distance from the sender Extra cares needed for multihop wireless networks! Number of transmissions per packet versus forwarding probability p in CRBcast Broadcasting Scheme # of Transmission per Packet Reliability Flooding 10000 1 PBcast 6999 0.99 CRBcast 2769 Two Scalable Methods Based on Relaying CRBcast Saves 72% and 60% energy in comparison with Flooding and PBcast, respectively. Rec 1 BEC (1) 1 Flooding Every node relays a packet that it receives for the first time Scalable Reliable (assuming ideal conditions) Disadvantage: Too much redundancy, Energy-Inefficient PBcast Every node relays a packet that it receives for the first time with a probability p Energy-efficient (inversely proportional with p) Disadvantage: Unreliable Rec 2 Rateless Coding BEC (2) Conclusion … … LT Encoding Rec i BEC (i) 1 The proposed broadcasting protocol (CRBcast): needs no information about the channel or the topology of the network needs no in-sequence packet delivery is easily extendable for mobile and lossy networks is well suited for multihop wireless networks is reliable, scalable, adaptable, and energy-efficient saves significant number of redundant transmissions in significant improvement over Flooding and PBcast Choose a degree d from a probability distribution. x1 x2 x3 x4 xk Information symbols … Choose d distinct message symbols uniformly at random. d XOR all the chosen symbols (bit wise) to produce an encoding (check) symbol. c1=x1+x2+x4 LT Decoding Encoding symbols Iterative decoding on k different packets ( is called overhead and is close to 1)