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Forward Error Correction

Forward Error Correction . FEC Basic Idea. Send redundant data Receiver uses it to detect/correct errors Reduces retransmissions/ NAKs Useful when RTT is high. Types of FEC . Two types of FEC Block codes (works on blocks/packets) Hamming codes, Reed-Solomon codes

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Forward Error Correction

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  1. Forward Error Correction

  2. FEC Basic Idea • Send redundant data • Receiver uses it to detect/correct errors • Reduces retransmissions/NAKs • Useful when RTT is high

  3. Types of FEC • Two types of FEC • Block codes (works on blocks/packets) • Hamming codes, Reed-Solomon codes • Convolutional codes (arbitrary length symbols/bits) • Viterbi codes

  4. Reed-Solomon Codes • Operates on blocks of m bits, each block is a symbol • Corrects symbol errors, not bit errors • Useful for correcting burst errors • E.g. 2 symbol error-correcting code for m=8 • Correct burst errors of 16 bits or less • Used for deep space communication, CDs, digital media

  5. (n,k)- Erasure codes • (n,k)-code means • k data packets • Encoded into n > k • Any k packets can be used to decode data • Tolerate up to n-k losses

  6. A simple example • Consider a simple (3,2) code • 2 Data bits a and b • Send the following 3 symbols • a • b • a XORb • Any 2 out of 3 symbols can now be used to decode all data • In general, coding is done over a finite field

  7. Recall TCP congestion control • Congestion control • Increase linearly if no packet loss • Decrease to half if packet loss Congestion 150 Kbps Channel error TCP sending rate 100 Kbps 50 Kbps Time t2 t0 t1

  8. Data vs. Redundancy tradeoff • Optimizing Forward Error Correction (FEC) coding rate for TCP • Trade-off between channel rate and packet error probability • What is the optimal coding rate for TCP? • Active research topic

  9. TCP packet DATA DATA FEC FEC Radio block Coded channel rate Packet error probability Coding rate Coding rate Coding trade-off: rate vs. error

  10. Coding rate vs throughput Channelrate = 128Kbps Optimal coding rate TCPthroughput (Kbps) Codingrate ( )

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