N=10000, k=2000 packets , =1.03

1. N=10000, k=2000 packets, =1.03 poptwpgiant 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) 2000 packets One packet 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 DATA, max(i,j) packets ADV 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) Simulation Results Our Proposal: CRBcast • Motivation • An easy, energy-efficient, and scalable broadcasting scheme • Providing reliability with little penalty • Low complexity • Require no optimization and no topology information 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 • CRBcast Saves 72% and 60% energy in comparison with • Flooding and PBcast, respectively. Two Scalable Methods Based on Relaying Rec 1 1 0 BEC (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 relaysa packet that it receives for the first time with a probability p • Scalable • Energy-efficient (inversely proportional with p) • Disadvantage: Unreliable Rec 2 Rateless Coding 0 BEC (2) Conclusion … … LT Encoding Rec i BEC (i) 1 0 • 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. Information symbols x1 x2 x3 x4 xk … • 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)