1. 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)