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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 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 • Example P=1E-9, n=1500*8, F=1E-5 • Example P=1E-3, n=500, F=0,4
Gilbert Model No errors in state (good) 1 Bernoulli model in state (bad) 2 (BER=1-h)
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
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)
Elliot Model Bernoulli model in state 1 (BER=1-k) Bernoulli model in state 2 (BER=1-h)
BEP for the Elliot Model Assumed: 1-h >> 1-k h and transition probabilities determined as for the Gilbert model K determined from BEP
The McCullough model Random error state Bursty error state State change allways on error
The Fritchman model Transition between error free state prohibited (for tractability)
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
Measured Error Cluster Probabilities Straight line -> geometric -> only one dominating eigenvalue -> only one errorstate