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Markovian Error Models

Markovian Error Models. Based on Jeffrey S. Slack FINITE STATE MARKOV MODELS FOR ERROR BURSTS ON THE LAND MOBILE SATELLITE CHANNEL. Bernoulli model. Independent bit errors Bit Error Rate (BER)=P Frame Error Rate (FER)=F N: bits per frame F=1-(1-P) n ¼ n P

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Markovian Error Models

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  1. Markovian Error Models Based on Jeffrey S. Slack FINITE STATE MARKOV MODELS FOR ERROR BURSTS ON THE LAND MOBILE SATELLITE CHANNEL

  2. Bernoulli model • Independent bit errors • Bit Error Rate (BER)=P • Frame Error Rate (FER)=F • N: bits per frame F=1-(1-P)n ¼ n P • Example P=1E-9, n=1500*8, F=1E-5 • Example P=1E-3, n=500, F=0,4

  3. Signal strength and bursty errors

  4. Gilbert Model No errors in state (good) 1 Bernoulli model in state (bad) 2 (BER=1-h)

  5. Determining Model Parameters • Match average BER • Match Error Gap Distribution U(n)=P(00..0) (at least n good bits in row) • Match Block Error Probability P(m,n)=probability of m errors in block of n bits

  6. Mapping Transition Probabilities to u(n) and P(m,n) P11,P12,P21,P22! u(n),P(m,n) P*11,P*12,P*21,P*22Ã u*(n),P*(m,n)

  7. Matching Error Gaps

  8. Matching Block Error Probabilities

  9. Elliot Model Bernoulli model in state 1 (BER=1-k) Bernoulli model in state 2 (BER=1-h)

  10. BEP for the Elliot Model Assumed: 1-h >> 1-k h and transition probabilities determined as for the Gilbert model K determined from BEP

  11. Matching Error Gaps

  12. Matching BEP

  13. The McCullough model Random error state Bursty error state State change allways on error

  14. BEP for the McCullough model

  15. Estimation

  16. Results

  17. Best k-value

  18. The Fritchman model Transition between error free state prohibited (for tractability)

  19. PBA PB Error Gap Probabilities PAB PA PB=I PAB=0 • B-states are now attractive • Probabilities for staying in A-states are the same for the two transition matrices

  20. Error Gap Probabilities

  21. Error Gap/Cluster Probabilities

  22. Measured Error Cluster Probabilities Straight line -> geometric -> only one dominating eigenvalue -> only one errorstate

  23. Block Error Probabilities

  24. Estimation

  25. Matching Error Gap

  26. Matching Block Errors

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