Network Coding vs. Erasure Coding: Reliable Multicast in MANETs Atsushi Fujimura*, Soon Y. Oh, and Mario Gerla *NEC Corporation University of California, Los Angeles

Page 2 Motivation Tactical networks require high reliability of multicast communications for effective mission accomplishment Both Network coding (NC) and erasure coding (EC) can increase reliability in lossy networks Which coding scheme is more reliable and efficient for MANETs?  “The jury is still out”

Page 3 Previous Works Finding performance gain in ad hoc multicasting – “Performance of Network Coding in Ad Hoc Networks” J-S. Park et al. Finding maximum throughput gain in multicast – “Reliability Gain of Network Coding in Lossy Wireless Networks” M. Ghaderi et al. Derive asymptotic bound for reliability gain – Previous works are theoretical analytical studies based on simple topologies  Our work is: – Simulation study – Implementing Network coding and Erasure coding – Realistic topology

Page 4 NC and EC Implementation Both randomly and linearly encode: – Block coding: stream of packets is split into blocks and encoded – Coefficients are randomly drawn from a finite field – Receivers reconstruct original data Erasure Coding Example

Page 5 Network Coding Example

Page 6 NC and EC Implementation Probabilistic Forwarding: – In both NC and EC each intermediate nodes forwards with probability f Forwarder generates random number x Compare x and drop rate d If (x < d) forwarding received packet Otherwise drop packet Packet Drop

Page 7 NC and EC Implementation Network CodingErasure Coding Coding at Source ( Rate c = k/n ) Coding rate c = 1. A source does not generate redundant packets k original packets are encoded into n > k source encoded packets, c < 1 Encoding at Intermediate Nodes YesNo Buffering and Forwarding Intermediate nodes enqueue innovative packets for re-encoding Intermediate nodes forward only non- duplicated packets

Page 8 Simulation Settings Qualnet implementation – Random linear coding – 2Mbps channel bandwidth, 376m radio range – b MAC and PHY – 1KB/s traffic Two topologies – Grid topology – Random topology Performance Metrics – Packet Delivery Ratio (PDR) – Normalized Packet Overhead

Page 9 Grid Topology Setting Grid Topology – One source and three receivers – Each node has r redundant paths (except the 1 st hop) – h: Number of hops from a source to receivers Receivers R S RR h Source r

Page 10 Simulation (Grid Topology) EC coding rate ranges between c=1 and c=1/6 EC requires twice as much line overhead to achieve the same delivery ratio as NC Packet delivery ratio when h =5 Overhead in term of h when f =1

Page 11 Simulation (Grid Topology) EC Delivery ratio is very sensitive to hop number (while NC holds its performance variation smaller) Packet drop probability on a link (d) has more impact on NC achievable delivery ratio Packet delivery ratio for varying hop # Packet delivery ratio for variable packet drop rate, h=5

Page 12 Analysis (Grid Topology) Single-hop models for NC (left) and EC (right) Different packets (NC) and duplicated packets (EC) fff S２S２ R 1-d fff S R S１S１ S３S３ R S RR Network coding case Erasure coding case

Page 13 f : forwarding probability d : packet drop probability k : generation size n : encoded packets at the source c : code rate (=k/n) h : number of hops r : number of redundant paths Analysis (Grid Topology) N NC, N EC : Potential number of innovative packets a node can receive (based on the single-hop models) Redundant paths r help N NC increase (add new redundancy) N EC increases according to code rate c (suffering overhead)

Page 14 f : forwarding probability d : packet drop probability k : generation size n : encoded packets at the source c : code rate (=k/n) h : number of hops r : number of redundant paths Analysis (Grid Topology) Packet drop (d) should have an equal impact on N NC and N EC But… Small N NC (1) also reduces the probability of generating innovative packets (differs from our assumption)  Redundancy to the first hop will help NC

Page 15 Random Topology 50 nodes including one source and 10 multicast members Nodes are randomly distributed in a square field Node density = average number of nodes within the transmission range (376m)

Page 16 Simulation (Random Topology) EC suffers much more overhead (similar to the results in Grid Topology) As for grid topology, EC delivery ratio equals NC delivery ratio between c =1/3 and c=1/2 Packet delivery ratio and overhead when the node density is 12

Page 17 Simulation (Random Topology) Lower node density reduces the redundant paths  disadvantage for NC Lower node density increases the number of hops  disadvantage for EC  Similar impact on both NC and EC

Page 18 Simulation (Random Topology) Packet Drop decreases delivery ratio, but more significant in NC than EC Node mobility helps both NC and EC recover from high packet drop rate Packet drop probability (d) = 0.4 Packet delivery ratio with drip rate and mobility when node density is 12

Page 19 Summary Compared NC and EC in MANETs NC can achieve high delivery ratio with much less overhead Future Work Implementation of joint EC and NC scheme Extension to vehicular applications

Page 20 Thanks