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Ch11Sec3_1

Ch11Sec3_1 - THE FIBER FORUM Fiber Optic Communications...

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Dr. Joseph C. Palais 11.3 1 THE FIBER FORUM Fiber Optic Communications Dr. JOSEPH C. PALAIS PRESENTED BY

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Dr. Joseph C. Palais 11.3 2 Section 11.3 Error Rates
Dr. Joseph C. Palais 11.3 3 Bit-Error Rate (BER) Fractional number of detection errors. The units of BER are errors per bit. Example: If the BER is BER = 0.001 = 10 -3 BER = 1/1000 There is, on average, one error for every 1000 bits received. The probability of an error (P e ) equals the BER.

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Dr. Joseph C. Palais 11.3 4 If R = data rate (bits/sec), the number of errors per seconds is obviously: RP e [(bits/s) x (errors/bits) ] = errors/s Example: If the data rate is R = 45 Mbps and the probability of error is P e = 10 -9 , how many errors/sec are there? Solution: RP e = 45 x 10 6 x 10 -9 = 45 x 10 -3 = 0.045 errors/s For example, every 100 seconds there are (on the average) 4.5 errors or 1 error every 1/0.045 = 22.2 s.
Dr. Joseph C. Palais 11.3 5 We will separately compute the error rates for thermal- noise limited and shot-noise limited systems.

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Dr. Joseph C. Palais 11.3 6 11.3.1 Thermal-Noise-Limited Error Rate Consider the following waveforms: Ideal receiver current 1 0 1 i s 1 0 1 t Actual current t i s i = i s + i N = i s + i NS + i NT The sampling times are indicated in green. i i
Dr. Joseph C. Palais 11.3 7 For the thermal-limited case: i NT >> i NS Sampled current (sample and hold): Threshold current i s t Perceived data (comparator) 1 0 0 t Error t

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Dr. Joseph C. Palais 11.3 8 1. 1’s are perceived as 0’s when the noise current is out of phase with the signal current, lowering the total current. 2. 0’s are perceived as 1’s when the noise current exceeds the threshold current.
Dr. Joseph C. Palais 11.3 9 What is the optimum value of the threshold current? If 1’s and 0’s are equally likely, The optimum threshold is 0.5 i S . Derivation of Probability of Error P e Let the threshold current be set as ki s where 0 < k < 1

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Dr. Joseph C. Palais 11.3 10 Case I: Assume a binary 1 is transmitted. Then i = i S (ideally) An error occurs if (i S + i N ) < ki S i N < - i S (1 - k) Note that this corresponds to a negative (out-of-phase) current. Case II : Assume a binary 0 is sent. An error occurs if i N > ki S
Dr. Joseph C. Palais 11.3 11 For Case I, the probability of error is: Prob [ i N < - i S (1 - k) ] x Prob [1] The product rules applies to the joint probability of independent events. Notation: Prob[y] = Probability of event y occurring. Also, use the shorthand notation: Prob [y] = P[y] For equally likely 0’s and 1’s we can write: P[1] = P[0] = 1/2

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Dr. Joseph C. Palais 11.3 12 For Case II, the probability of error is Prob [ i N > ki S ] x Prob [0] The total probability of error is the sum of the probabilities of the various ways errors can occur.
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