NETWORK CODING OVERHEAD Yalin Saguyu y-saguyu@northwestern.eu Department of Electrical Engineering an Computer Science Northwestern University Joint work with M. Rimensberger, M. L. Honig, an W. Utschick 1
Introuction & Motivation Network coing optimizes multicast rates to max-flow min-cut boun (Ahlswee, et. al. 00). Plain routing is not optimal & Linear network coing is sufficient (Li, et al. 03, Koetter-Mear 03). Typical assumption: Destinations know how packets are network-coe. Protocol Information Heaer? Data Symbols Limiting effects of network coing overhea. Joint channel coing/training for robust network coing. 2
Network Coing Overhea Network: Source: X Any Destination: Y = G X network coing matrix (elements from finite fiel F q ) Distribute solution: Ranom network coing (Ho, et. al 06). Communicate G to estinations in packet heaer: G Data Challenge: Decoing impossible, if error/erasure in G. 3
System Moel for Overhea Analysis Question: What is overhea for reliable communication of G & ata? Source Network Destinations N Packets Length D N D N L ranom network coing en-to-en channel (error/erasure) Unknown topology & G (i.i. assumption). 4
Network Coing Meets MIMO: Training Approach Detection of network coing matrix G MIMO channel estimation. Source transmits known training sequence. Destination receives. Rows of are encoe by Interpretation: is a coe generator matrix (e.g., MDS coe) Rows of are the transmitte packets 5
Encoing with Training Separate training an coing (STC). training overhea ata channel coe Joint training an coing (JTC). uncoe overhea ata joint encoing 6
Decoing Channel & Network Coes (1) Decoe channel coe: Ĝ Û for ranom network coing matrix for network-coe ata: U = G G S ( S: source packets) JTC: Jointly ecoe entire packet. STC: Separately ecoe training an ata parts. Maximum Likelihoo (ML) estimates (2) Decoe network coe: Ŝ Solve Û = Ĝ Ŝ for ata from ML estimates an. Ĝ Û 7
Throughput & Overhea Two types of ecoing error: Errors/erasures in packets Rank-eficient network coing matrix Ĝ Decoing probability P is erive via ranom coing bouns. En-to-en achievable rate: Λ * = max N, D N D L min P Overhea: O = L D L N : D : L : inepenent messages per transmission ata symbols per packet total packet length 8
Limiting Effects of Overhea Example 1: Combination network - Network Throughput Λ Μ : min-cut capacity optimal Ν Ν = Μ overhea kicks in 9
Throughput-Overhea Performance (Cont ) Example 2: Gri network source estination Each link carries M / 2 packets per time slot Fiel q = 2 8, 60 bits per packet Bit error probability 10 3 simulation analysis JTC: Joint training & coing ITC: Iniviual training & coing REF: Destination knows G analysis: Ranom coing boun on probability of successful ecoing simulation: Average error rates over ranom coing matrices & error events with MDS channel coes 10
En-to-En Distribute Network Coing Oblivious to network topology (mobility effects, malicious behavior, ). No nee to know network coing matrix G. Nee to know min-cut capacity (s.t. ) M N M N : inepenent messages per transmission Rate control: Aapt N base on estination feeback (ACK/NACK). N Increase, if channel & network coes are successfully ecoe. N Decrease, otherwise. 11
Conclusions Training can be combine with channel coing. Enables joint ecoing of ata an network coing matrix. Simplifies an balances protection of overhea. Network coing gain is limite by the necessary protocol overhea. Overhea grows with the min-cut capacity. Future Work: Extension to general error an erasure moels. Exploit reunancy in sequence of coing matrices. Aaptive training an feeback schemes to learn error statistics. 12