1. 1 Forward Error Correction Shimrit Tzur-David School of Computer Science and Engineering Hebrew University of Jerusalem

2. 2 Agenda Introduction The FEC algorithm ImplementationPerformance

3. 3 Introduction Loss of packets is a fact of life in computers networks. The usual approach to recover from losses is to retransmit missing packets on request. The presented approach is to add an error recovery mechanism that enable the receiver to recover all useful data without sending explicit request for missing packets. Such a mechanism can be implemented by applying a redundant encoding to the source data, so that even in presence of packet losses, sufficient information is conveyed to the receiver to allow successful reconstruction of the original data.

4. 4 Multicast Communication The possible lack of correlation between losses at different receivers can cause severe scalability problems. It will be helpful if in this situation, the receiver will enable to recover all useful data without sending explicit requests for missing packets.

5. 5 The goal The idea of this research is to show that under some circumstances, incorporating error correction schemes inside the TCP achieves better performance than that of retransmission schemes. Error correcting schemes for missing packets can be classified as (k, n) schemes, where k is the number of data packets in a FEC block and n is the number of all the packets in the FEC block (including data packets and the error correcting packets).

6. 6 Agenda Introduction The FEC algorithm ImplementationPerformance

7. 7 The FEC Algorithm Implemented by applying a redundant encoding to the source data. In presence of packet losses, sufficient information is conveyed to the receiver to allow successful reconstruction of the original data. Such an encoding is called erasure code.

8. 8 Erasure Code The idea: encode a set of k source data packets into a set of n > k encoded data packets. Any subset of k encoded packets allow the reconstruction of the original source. Such a code is called an (n, k) erasure code. The goal: produce the encoded packets given arbitrary values for k and n and make the encoding/decoding procedure sufficiently fast for practical use.

9. 9 Erasure Code – Cont.

10. 10 A Simple Erasure Code A polynomial of degree k-1 is completely specified by its value in k different points. Consider the source data packets as the coefficients of a polynomial P of degree k-1. The encoded packets are the values of P computed in n different points. The decoding: recover the coefficient of P given its values in k points. This code is called Vandermond code.

11. 11 Systematic Codes The transmission include a verbatim copy of the source data. No decoding effort is necessary in absence of errors. The Vandermond code is not systematic, but it can be turned into a systematic code by simple algebraic manipulations.

12. 12 Systematic Codes – Cont. - the coefficients - the values of the polynomial

13. 13 Vandermond matrix (G)

14. 14 Systematic Codes – Cont. Any minor of degree k extracted from this matrix is invertible. This property still holds if we do linear combinations of the columns. We can manipulate the matrix in such a way that the upper k rows become the identity matrix. After the transformation: G*X will give us -  We have obtained a systematic code.

15. 15 The encoding The source data: G is an (n,k) matrix, any subset of k rows of G, G`, is an invertible matrix. The sender sends, but the receiver gets y which contains k values from it.  The encoding data is:

16. 16 The decoding The original data can be reconstruct by using k equations on the known values in y.

17. 17 Agenda Introduction The FEC algorithm ImplementationPerformance

18. 18 Implementation End-to-end error correction should be addressed at the transport layer, since it responsible for packet reliability. In the handshake process, the connection initiator add a FEC flag inside the TCP options inside the ‘Syn’ packet. If the receiver also knows how to deal with FEC, its ‘Syn-Ack’ packet will also contain the FEC flag. The sender now knows that it can encode its data.

19. 19 Sender For each new packet, it adds the FEC header. The FEC header contains n, k and the index of the packet in the block. It saves the packet payload in the FEC buffer. It sends the packet. When it sends a full data block (k packets), it encodes the data using the data in FEC buffer, creates the FEC packets and sends them as well.

20. 20 Sender – Pseudo Code Sendmsg(buf){ while (length(buf) > 0) create new packet fec_index++ add fec header to packet {fec_index, k, n} data_len=min(mss, length(buf)) take data_len bytes from buf and add to the payload save payload in fec_buf send packet

21. 21 Sender – Pseudo Code – Cont. if fec_index == k for(i=k; i<n; i++) fec_payload=encode(fec_buf,i)create_fec_packet(fec_payload) send fec packet fec_index = 0; }

22. 22 Receiver For each packet that it gets, it pulls the FEC header. If this is redundant FEC packet it throws its payload, else it adds the packet to the FEC queue. If this is a FEC packet, it doesn’t send its payload to the application layer. If there is a block with up to n-k missing packets, it decodes it (using FEC queue), handles queues, and sends the reconstructed data to the application layer.

23. 23 Receiver – Pseudo Code dataqueue(packet){ get_fec_header (packet,fec_index, k, n) If (!redundand && !exist) add packet to fec_queue in the right order (by s.n.) If (fec_index > k) payload len = 0 payload len = 0

24. 24 Receiver – Pseudo Code – Cont. for (i = 0; i < n - k; i++) if there is a full block with ‘i’ holes if i == 0 delete block from queue breakelse payload [] = decode(fec_queue) simulating receiving the missing packets with the decoded payload delete block from queue break}

25. 25 Agenda Introduction The FEC algorithm ImplementationPerformance

26. 26 Performance The measurement were taken in the LAN, with n=9 and k=8. We compared the transferring time with files in sizes: 50MB, 100MB, 150MB and 200MB. We demonstrated packet loss by throwing the picked packets at the receiver side. We made the measurements with different loss probabilities: 0.025, 0.05, 0.075, 0.01, 0.0125, 0.015, 0.0175, 0.02, 0.025, 0.03, 0.035, 0.04.

27. 27 50MB File

28. 28 100MB File

29. 29 150MB File

30. 30 200MB File

31. 31 Conclusions As we can see, all the graphs show better results until the loss probability reaches to 3%. In loss probability higher than 3%, the probability to lose the FEC packets increases, in this case there is no decoding process to reconstruct it. The receiver can lose more than one packet in a block, in this case it needs to wait until it gets one of the missing packets (by retransmission). If one of the FEC packets is lost, and another packet in the next block is lost, we reconstruct the packet in the next block, but we still can’t transfer the data to the application layer.

32. 32 TODO The system should sense its traffic and if there are losses in which the FEC is useful (and still TCP friendly) turn it on. If there is a high percentage of losses, turn off the FEC algorithm. The system should be able to handle change of n and k during a connection.

33. 33 THE END