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
Theorem: G(N,r,p) is a connected dominating graph if and only if p>pth, where pth
is given by
p thr 2 ln( p th N )  ( N )
 Objective
 Broadcasting in multihop wireless networks
 Energy-Efficient
 Reliable
 Scalable
 Low Complexity: Requires no topology knowledge

A
as N  
N
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  (N)   as N  
 Motivation
 Updating software in already deployed sensor/actuator networks
 Broadcasting route query packets in reactive routing schemes
 Key revoking of compromised keys
One packet
 Some Related Work
 Flooding [Obraczka99], Probabilistic Broadcast [Tseng99],
Counter-Based Scheme [Tseng99], GARUDA [Park04], Dominating Set
Based Scheme [Stojmenovic02], …
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
About 7000 transmissions per packet
For 99% reliability
 Reliability decreases a lot
 P = 0.7 for 99% reliability
 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:
Almost all
nodes
receive
the packet
REQ, j packets
DATA, max(i,j) packets
ADV
pth =0.43
REQ, i packets
 Our Approach
 Employing an efficient erasure coding (Rateless Coding) to recover for
losses in conjunction with a probabilistic relaying
Reliability (fraction of nodes that receive all packets)
versus forwarding probability p in PBcast
N = 10000, r = 25, A = 1000x1000
Number of transmissions per packet
versus forwarding probability p in PBcast
(i)
(ii)
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
 Minimum Connected Dominating Set (MCDS)
Finding MCDS is NP hard!
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10
8
6
4
2
0
 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
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2
4
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10
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14
Two Scalable Methods Based on Relaying
 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
 Scalable
 Energy-efficient (inversely proportional with p)
 Disadvantage: Unreliable
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20
 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
popt w pgiant
 # 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
Number of transmissions per packet versus forwarding probability p in CRBcast
 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!
BEC (1)
Rateless
Coding
BEC (i)
Choose a degree d from a probability distribution .
1
…
symbols
at random.
 XOR all the chosen symbols (bit wise) to
d
produce an encoding (check) symbol.
LT Decoding

c1=x1+x2+x4
# of Transmission per Packet
Reliability
Flooding
10000
1
PBcast
6999
0.99
CRBcast
2769
1
CRBcast Saves 72% and 60% energy in comparison with
Flooding and PBcast, respectively.
Conclusion
Rec i
0
x1 x2 x3 x4 xk Information
 Choose d distinct message symbols uniformly
Broadcasting Scheme
Rec 2
0
BEC (2)
LT Encoding

Rec 1
1
0
…
 Nodes with only Relaying Capability
20
N=10000, k=2000 packets, =1.03
…
Optimal Solution
(iii)
Encoding symbols
Iterative decoding on k different packets ( is called overhead and is close to 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