Forward Error Correction

1
Forward Error Correction

• Shimrit Tzur-David
• School of Computer Science and Engineering
• Hebrew University of Jerusalem

2
Agenda

• Introduction
• The FEC algorithm
• Implementation
• Performance

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.

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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
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
Agenda

• Introduction
• The FEC algorithm
• Implementation
• Performance

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
Erasure Code

• The idea encode a set of k source data packets
  into a set of n gt 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.

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Erasure Code Cont.
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.

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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.

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Systematic Codes Cont.
- the coefficients -
the values of the polynomial
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Vandermond matrix (G)
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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 GX will give us -
• ? We have obtained a systematic code.

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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
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The decoding

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

17
Agenda

• Introduction
• The FEC algorithm
• Implementation
• Performance

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.

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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.

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Sender Pseudo Code

• Sendmsg(buf)
• while (length(buf) gt 0)
• create new packet
• fec_index
• add fec header to packet fec_index, k, n
• data_lenmin(mss, length(buf))
• take data_len bytes from buf and add to the
  payload
• save payload in fec_buf
• send packet

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Sender Pseudo Code Cont.

• if fec_index k
• for(ik iltn i)
• fec_payloadencode(fec_buf,i)
• create_fec_packet(fec_payload)
• send fec packet
• fec_index 0

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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 doesnt 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.

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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 gt k)
• payload len 0

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Receiver Pseudo Code Cont.

• for (i 0 i lt n - k i)
• if there is a full block with i holes
• if i 0
• delete block from queue
• break
• else
• payload decode(fec_queue)
• simulating receiving the missing packets
  with the decoded payload
• delete block from queue
• break

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Agenda

• Introduction
• The FEC algorithm
• Implementation
• Performance

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Performance

• The measurement were taken in the LAN, with n9
  and k8.
• 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.

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50MB File
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100MB File
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150MB File
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200MB File
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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 cant
  transfer the data to the application layer.

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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.

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• THE END