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Once digitized, a signal can be communicated 100 meters or internationally, typically web no additional degradation as long as Me signal on each intermediate link is maintained above threshold. For example, We current predominantly aB digital public telephone network permits local, national, and international cans usually of equal quality while the old analog network often degraded badly on national and international calls. Similarly, Me evolving commercial digital television win provide exceptional quality TV to most of Me public; however, viewers on the fringe of the signal coverage area may no longer get a chewable picture (without cable or over source) because the weaker RF signal win create a badly detenoratM (unusable) video signal when below Ashore. Fringe area viewers of cunTent analog TV simply get a noisy, snowy picture. ITS will undoubtedly evolve to digital TV to permit sharing of high quality full motion video images among jurisdictions regardless of location. Our focus win be on digital communication networks as this is He modern trend Cat industry is increasingly evolving toward. Digital networks are support by He most cost-effective components, equipment, systems, and services. Additionally, designers for digital communication are more readily available. A.2.2 Theoretical and "In Practice" Capacity of Digital Communication Mediums In 194S, C. E. Shannon published a seminal paper on "A Mathematical Theory of Communication" In He Bell System Technical journal. It established the ~eoredcal bit rate of a digital communication channel. It also established a relationship between: BR = BW*Iog2 ~ ~ + STIR ); where (eq. A.2.2-~) I. BR is He ~eoredcal maximum digital bit rate possible on a communication channel. 2. BW is He available communication channel band in Hertz. c:`NCHR~\ NCHRP3-51 Pnase2F'nalReport A2 -

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3. SNR is Me signal-to-noise ratio of We desired source digital signal to corrupting "white" noise ("white noise" for statistical analysis is uncorrelated gaussian samples). 4. Note: SNR = lO^(SNRDJ1O) as most SNR are specified in dB. [Also note Me inverse: SNRDB = JO*IOgIO (SNR)~[Note: X^Y = XY] The proof of this relationship is based on very sophisticated mathematics and is beyond Me scope of this work. It should be noted Mat Shannon, in his derivation of this limit, used very clever statistical and mathematical techniques Hat did not require him to develop the actual techniques to achieve He predicted limidng performance. Thus, communication practitioners continually strive in R&D for the theoretical performance limim for various mediums. They have yet to achieve Hem in practice; however, it is He measure by which communications engineers judge He efficiency of utilization of Heir con~mun~cadon channels. As an example, a 25 kHz Bandwidth (BOO) RF channel at 10 and 15 dB SNR, can support bit rates of: BR = 25 kHz * logic ~ ~ + 10~5~~/ log~0~2) = 125.7 kbps Typical RF Channels BR = 25 kHz * logic ~ ~ + 10~~~/ log~0~2) = 25.0 kbps In practice, bit rates of 4.8 to 19.2 kbps are being obtained over 25 kHz radio channels. RF bit rates in practice are usually substantially less Han Be theoretical limits due primarily to extensive portable transceivers dial cannot employ specially efficient modulation techniques due to battery drain requirements, small equipment size and weight requirements, and cost constraints. Fixed RF transceivers without these constraints can be more speck y efficient and therefore more closely approach these theoretical limits. In fact, microwave radio does employ specmally efficient modulation techniques. Similarly, an SMFO fiber typically has a bandy ink over 10 GHz and a SNR of over 40 DB and can support a BR over: BR= 10 GHz * logic ~ ~ + 104~~/log~0~2) = 132.9 Gbps L:wa~P ~NCHRP3-51 Phase2FmalReport A2-5

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In practice, He current long distance fiber network is 2.488 Gbps (OC48) and is evolving to 10 GHz (OC-192). The limiting factors in SMFO are the electronics and optical components with speed to support the potential of the optical channel. In realibr, the available bandwidth and bit rate of fiber is adequate without near tenn concern for efficiency. The modem industry appears to have most closely approached He attainable limits predicted by Shannon's theory, thus it is instructive to review modem performances achieved in practice and to note that the recent ITU V.34, 28.8 kbps starboard, over a 3500 Hz public circuit, is operating close to the limit. Figure A.2~2-1 plots bandwidth required versus required signal-to-noise (SNR) for popular modem bit rates. Also, depicted on He graph is He actual range of operation in practice for He following modems: 1. Bell 202 (Model 400), 1200 bps modem (1970 origins) 2. ITU V.32' 9600 bps modem (1984 origins) 3. ITU V.34, 28,800 bps modem (1994 ongins) The range of operation must be above and to the right of the appropriate bit rate curve. As can be observed, the modem industry, through extensive R&D activities, has improved (or moved) the range of operation closer to the theoretical bit rate limit for bandwidth and SNR. The V.34 will, in fact, only work over higher quality dial-up circuits and must fall back to lower speeds on lower quality circuits (e.g., bandwidth constraints or inadequate SNR). Shannon's theory predicts this requirement. Table A.2.~! presents a matrix of popular ITS comn~un~cation mediums and He ~eoredcal maximum bit rate. It should be noted Hat fiber does not achieve comparable spectral efficiency In terms of bits/Hertz Hat is achieved with wireline modems. With the exception of microwave, wireless is also usually less specify efficient ~:~\ N~3-51 IF A2-6

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