This ATM determines the probability of sync, false sync, and the probability of loosing sync for an 11 bit and 6 bit frame sync code. The number of bits/frame range from 1344 to 4032. The amount of data lost during loss of sync is also determined.prepared by H. Lanning

Lanning, H. E.

USRA Houston Repository

BENDIX SYSTEMS DIVISION ANN ARIOR,MICH NO. ATM- 444 REV.NO. Active Seismic Frame Synchronization PAGE 1 OF This ATM determines the probability of sync, false sync, and the probability of loosing sync for an 11 bit and 6 bit frame sync code. The number of bits I frame range from 1344 to 4032. The amount of data lost during loss of sync is also determined. Prepared by __ ___.;/:......;.._._4_t2_· -r_'-_<?_~_:J-:7~:J...-­H. Lanning (/ Approved by <j[/.i?Mf..d.J r· Hutton 5 PAGES 8/4/66 1. Introduction BENDIX SYSTEMS DIVISION ANN ARIOR,MICH NOATM- 444 Active Seismic Frame Synchronization PAGE 2 REV.NO. OF 5 In order to minimize the probability of falsely synchronizing on a data word, the frame sync code length should be made as large as possible and the number of data bits/frame should be kept small. In the active seismic mode of operation, maintaining this high density of sync bits to data bits is not feasible and a compromise must be made. The selection of an 11 bit sync word with 1344 bits/frame was origin-ally chosen in order to optimize the experiment performance within the con-straints of a 10600 bps data rate. This selection gave a reasonably low probability of falsely synchronizing on data. As time went on, however, it was determined that even this density of sync bits to data bits was too high and improved experiment performance could be achieved by lowering this density. 2. Calculations The formulas used to calculate the probability of sync and the proba-bility of falsely syncing on data words were obtained from the literature* and are: e 1) : 2:= (~) px(l-p) n-x p s X- 0 where: p s -= Prob. of sync e =no. of allowed bit errors (0-9) n .;: length of sync code, bits p = prob. of bit error ( ~ 10-4) 2) PFs :. 1 - [- __!_ [ zn where: PFs = prob. of falsely syncing on data b = ratio of data bits to sync bits * Williard, M. W., PCM Synchronization, NTC, 1961 PAGES REV.NO. BENDIX SYSTEMS DIVISION ANN A R I 0 R, M t C H NO. Active Seismic Frame ..,.__A ... T ..... M.--_4.,.4.,.4...__ ...... ______ _ 8/4/66 Synchronization 3 5 PAGE OF Note that the probability of falsely syncing in the code overlap region was not considered since it is much lower than the probability of syncing on data. After sync is obtained, a 3 bit frame sync window is activated and the decem is programmed to check the incoming bit stream only when the frame sync word occurs. Since the probability of syncing on the code word is P s' the probability of not syncing or of loosing sync is PLs = 1 ... P s· The previously mentioned calculations have been made for a probability of bit error of 10-4, 11 and 6 bit code lengths, and 1344-4032 bits/frame. The results of the calculations are presented in Table 1. From Table 1, it can be seen that the proper choice of e (the no. of allowed bit errors) should be o for synchronization and e • 1 for indicating loss of sync. Using these values, the probability of sync is • 999 for the 11 bit code and the probability of loosing sync is 2 x 1 o-6. Since the probability of loosing sync is so lowJ a long resync time could be tolerated since loss of sync would occur very seldom. 3. Time Required to Indicate Loss of Sync Loss of sync is indicated after a preset correlation threshold is not exceeded for a preset number of frames. The preset correlation threshold can be set from 0-9 allowed bit errors. The number of times that the sync word is checked can be set at 0-19. If the sync word is not checked (set at 01 then when th• -::orrelator does not exceed the threshold, the decommutator immedi-ately starts the search mode and tries to resync. Since sync can be lost and not known until the next sync word appears, the maximum time required to indicate loss of sync is 1 frame length with an average of 0. 5 frame lengths. When the sync word is checked (1-19 times), the maximum time required to indicate loss of sync is equal to the number of frames checked plus 1. The average time is equal to the number of frames checked plus 0. 5. 4. Time Required to Resync After Loss of Sync Indicated Again, the number of allowed bit errors (0-9) and the number of frames to be checked must be set into the decommutator. After the decommutator indicates loss of sync as described in section 3, the scanning mode is initiated. If the sync word is not checked (set at 0), then the maximum time required to resync is 1 frame length with an average of 0. 5 frame lengths. When the sync word is checked (1-19 times), the average resync time per false alarm is equal to the number of frames checked plus 0, 5. PAGES 8/4/66 No. of No. of Bits/ Sync bits Frame n 11 1344 11 2688* 11 4032 6 1344 BENDIX SYSTEMS DIVISION ANN ARIOR,MICH NO. REV.NO. ATM-444 Active Seismic Frame Synchronization Table 1 No. of Prob. of Allowed Pro b. False Bit Errors of Sync Sync e ps PFs 0 . 999 • 06 1 • 999998 . 5 0 • 999 . 12 1 . 999998 • 77 0 • 999 • 18 1 • 999998 • 89 0 • 9995 • 989 1 0 9999996 ~1 PAGE 4 OF 5 No. of Prob. of False Loosing Alarms Sync b PFs PLs 7 1o-3 60 2 x 1 o-6 24 Io-3 187 2 x 10-6 66 10-3 325 2 x 1 o-6 220 5 x 1 o-4 222 4 x 1o-7 * Max. bits/frame is 4096, However, Goddard recommends a max. of 2048. A waiver from them probably would be required to exceed 2098 bits. PAGES 8/4/66 BENDIX SYSTEMS DIVISION ANN ARIOI,MICH NOATM ... 444 Active Seismic Frame Synchronization 5 PAGE REV.NO. OF 5 If sync is lost by only ~ 1 bit, the decommutator will automatically PAGES resync in 1 bit time immediately after the correlator first does not exceed threshold. This is due to the 3 bit frame sync window built into the decommutator. 5. Amount of Data Lost When Sync is Lost If all frame checks are set to 0, then the total maximum lost time is 2 frames of data. Average lost time is 1 frame of data. The probability of resyncing correctly is a function of the code length and bits/frame. For an 11 bit code and 2688 bits/frame, the probability of false sync is 0. 12 with an average number of false alarms equal to 24. However, since the frame check is set on 0, these false alarms are never checked and we have a 0. 12 probability of not being synced correctly. This will be indicated during the next frame, however, as a probable loss of sync. If all frame checks are set to 1, then the average lost time is 1. 5+1. 5x24=37 frames of data for the above 11 bit code. The probability of falsely resyncing is about . 01. For the code of 11 bits and 2688 bits/frame and 1 error allowed for a loss of sync indication, the probability of loosing sync is quite small ( 2xl o-6). Hence, the number of times that 37 frames of data is lost would be very small. 

Active Seismic frame synchronization

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Active Seismic frame synchronization

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