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BATS: An efficient network coding solution for packet loss networks Raymond W. Yeung Institute of Network Coding The Chinese University of Hong Kong March 6, 2014 Presented at the IRTF Network Coding Research Group Joint work with Shenghao

  1. BATS: An efficient network coding solution for packet loss networks Raymond W. Yeung Institute of Network Coding The Chinese University of Hong Kong March 6, 2014 Presented at the IRTF Network Coding Research Group Joint work with Shenghao Yang (IIIS, Tsinghua U) R.W. Yeung (INC@CUHK) BATS Codes March 6, 2014, IRTF 1 / 21

  2. Patents Related to BATS code 1 US patent pending (US Patent App. 13/112,589) PCT application in China and some European countries R.W. Yeung (INC@CUHK) BATS Codes March 6, 2014, IRTF 2 / 21

  3. Achievable Rates s u t Both links have a packet loss rate 0 . 2. The capacity of this network is 0 . 8. Intermediate End-to-End Maximum Rate forwarding retransmission 0.64 forwarding fountain codes 0.64 R.W. Yeung (INC@CUHK) BATS Codes March 6, 2014, IRTF 3 / 21

  4. Achievable Rates s u t Both links have a packet loss rate 0 . 2. The capacity of this network is 0 . 8. Intermediate End-to-End Maximum Rate forwarding retransmission 0.64 forwarding fountain codes 0.64 network coding random linear codes 0.8 R.W. Yeung (INC@CUHK) BATS Codes March 6, 2014, IRTF 3 / 21

  5. Achievable Rates: n hops u 1 u n − 1 s · · · t All links have a packet loss rate 0 . 2. Intermediate Operation Maximum Rate 0 . 8 n → 0, n → ∞ forwarding network coding 0.8 R.W. Yeung (INC@CUHK) BATS Codes March 6, 2014, IRTF 4 / 21

  6. Complexity of Linear Network Coding T : length of a packet; K : number of packets Encoding: O ( TK ) per packet. Decoding: O ( K 2 + TK ) per packet. Network coding: O ( TK ) per packet. Buffer K packets. encoding network coding R.W. Yeung (INC@CUHK) BATS Codes March 6, 2014, IRTF 5 / 21

  7. Batched Sparse (BATS) Codes outer code inner code (network code) [YY11] S. Yang and R. W. Yeung. Coding for a network coded fountain. ISIT 2011, Saint Petersburg, Russia, 2011. R.W. Yeung (INC@CUHK) BATS Codes March 6, 2014, IRTF 6 / 21

  8. Encoding of BATS Code: Outer Code Apply a “matrix fountain code” at the source node: Obtain a degree d by sampling a degree distribution Ψ. 1 Pick d distinct input packets randomly. 2 Generate a batch of M coded packets using the d packets. 3 Transmit the batches sequentially. b 1 b 2 b 3 b 4 b 5 b 6 · · · · · · X 1 X 2 X 3 X 4 � � X i = G i = B i G i . b i 1 b i 2 · · · b id i R.W. Yeung (INC@CUHK) BATS Codes March 6, 2014, IRTF 7 / 21

  9. Encoding of BATS Code: Inner Code The batches traverse the network. Encoding at the intermediate nodes forms the inner code. Linear network coding is applied in a causal manner within a batch. · · · , X 3 , X 2 , X 1 · · · , Y 3 , Y 2 , Y 1 network with linear s t network coding Y i = X i H i , i = 1 , 2 , . . . . R.W. Yeung (INC@CUHK) BATS Codes March 6, 2014, IRTF 8 / 21

  10. Belief Propagation Decoding 1 Find a check node i with degree i = rank( G i H i ). 2 Decode the i th batch. 3 Update the decoding graph. Repeat 1). b 1 b 2 b 3 b 4 b 5 b 6 G 1 H 1 G 2 H 2 G 3 H 3 G 4 H 4 G 5 H 5 The linear equation associated with a check node: Y i = B i G i H i . R.W. Yeung (INC@CUHK) BATS Codes March 6, 2014, IRTF 9 / 21

  11. Precoding Precoding by a fixed-rate erasure correction code. The BATS code recovers (1 − η ) of its input packets. Precode BATS code [Shokr06] A. Shokrollahi, Raptor codes, IEEE Trans. Inform. Theory, vol. 52, no. 6, pp. 25512567, Jun. 2006. R.W. Yeung (INC@CUHK) BATS Codes March 6, 2014, IRTF 10 / 21

  12. Complexity of Sequential Scheduling Source node encoding O ( TM ) per packet O ( M 2 + TM ) per packet Destination node decoding buffer O ( TM ) Intermediate Node network coding O ( TM ) per packet T : length of a packet K : number of packets M : batch size R.W. Yeung (INC@CUHK) BATS Codes March 6, 2014, IRTF 11 / 21

  13. Inactivation Decoding BATS codes with M = 32 and q = 256. coding overhead inactivation no. K average max min average max min 1600 2.04 16 0 94.0 119 72 8000 6.30 77 0 215.5 268 179 16000 26.58 1089 0 352.2 379 302 R.W. Yeung (INC@CUHK) BATS Codes March 6, 2014, IRTF 12 / 21

  14. Tradeoff M = 1: BATS codes degenerate to Raptor codes. Low complexity No benefit of network coding M = K and degree ≡ K : BATS codes becomes RLNC. High complexity Full benefit of network coding. Exist parameters with moderate values that give very good performance R.W. Yeung (INC@CUHK) BATS Codes March 6, 2014, IRTF 13 / 21

  15. Experiment setting s u t Packet loss rate 0 . 2. Node s encodes K packets using a BATS code. Node u caches only one batch. Node t sends one feedback after decoding. R.W. Yeung (INC@CUHK) BATS Codes March 6, 2014, IRTF 14 / 21

  16. Experiment setting R.W. Yeung (INC@CUHK) BATS Codes March 6, 2014, IRTF 15 / 21

  17. Experiment setting R.W. Yeung (INC@CUHK) BATS Codes March 6, 2014, IRTF 16 / 21

  18. Experiment setting Sender/receiver: a laptop with open source Atheros wireless drivers. Relay: one wireless router with Atheros chipset running OpenWrt (about 150HKD/20USD) WiFi 802.11 b/g/n at 2.4GHz Sender’s rate is set to 1 Mb/s to reduce the effect of the router’s low computation power. R.W. Yeung (INC@CUHK) BATS Codes March 6, 2014, IRTF 17 / 21

  19. Compare with TCP Average rate (Kb/s) BATS w/ recoding 592.86 BATS w/o recoding 530.65 TCP (normal 802.11) 420.33 R.W. Yeung (INC@CUHK) BATS Codes March 6, 2014, IRTF 18 / 21

  20. Application: vehicular ad-hoc network R.W. Yeung (INC@CUHK) BATS Codes March 6, 2014, IRTF 19 / 21

  21. Application: mobile ad-hoc network R.W. Yeung (INC@CUHK) BATS Codes March 6, 2014, IRTF 20 / 21

  22. Summary BATS codes provide a digital fountain solution with linear network coding: Outer code at the source node is a matrix fountain code. Linear network coding at the intermediate nodes forms the inner code. Prevents BOTH packet loss and delay from accumulating along the way. The more hops between the source node and the sink node, the larger the benefit. R.W. Yeung (INC@CUHK) BATS Codes March 6, 2014, IRTF 21 / 21

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