� ECEN 5032 Data Networks Physical Layer Peter Mathys mathys@colorado.edu University of Colorado, Boulder Data Networks, Physical Layer, c 1996–2005, P . Mathys – p.1/37
✠ ✡ � � ☞ ✁ ☞ ☛ ✂ ✄ ✁ ✡ ✟ � Maximum Data Rate Nyquist’s result (1924): The maximum data rate of a noiseless signal with levels and bandwidth is maximum data rate bits/sec ☎✝✆✞ Shannon’s result (1948): Channel Coding Theorem . For a given noisy channel there exists a code that will permit error-free transmission at rate , provided , where is the channel capacity. Data Networks, Physical Layer, c 1996–2005, P . Mathys – p.2/37
☛ ✂ � � � ✂ ☛ ✞ ✂ ✞ ✂ ✂ ✡ ✡ ✂ Binary Symmetric Channel Transition probability (probability of error). ☎✝✆ ✟✝✠ ☎✝✆ ✟✝✠ ✁✄✂ ✁✄✂ Data Networks, Physical Layer, c 1996–2005, P . Mathys – p.3/37
✡ ✡ ✠ ✡ ✂ � ☞ ✞ ✡☛ ✠ ✂ ✞ ☞ ✠ ✂ ✞ ✠ ✡ ✂ � � ✡ ✂ ✠ ✡ ✂ ☞ ✠ ✂ ✞ ✡ ✡ ✠ ✂ ✠ � ☞✌ ☞ ✞ ☞ ✠ ✡ ✂ ☞ � ✄ � ✁ ✟ ✟ � � ✂ ✄ � ✂ ☎ � ✄ � ✂ ✁ � ✞ ✂ ☞ ☞ ✂ � ✂ ☎ � � ✁ ✄ � ✟ ✟ ✂ ✞ � � ✞ ✄ Channel Capacity of BSC The capacity of the binary symmetric channel (BSC) is bits/use ✆✞✝ ✆✞✝ where is the probability of error and is the binary entropy function for . Examples: bits/use. bits/use. bits/use. Data Networks, Physical Layer, c 1996–2005, P . Mathys – p.4/37
� BSC Capacity Capacity C = 1 − H(p) of Binary Symmetric Channel 1 0.9 0.8 p=0.1, C=0.531 p=0.01, C=0.919 0.7 p=0.001, C=0.989 Capacity C [bits/use] 0.6 0.5 0.4 0.3 0.2 0.1 0 −3 −2.5 −2 −1.5 −1 −0.5 0 Transition Probability log 10 p Data Networks, Physical Layer, c 1996–2005, P . Mathys – p.5/37
✂ ✞ ✁ ✡ ✝ ✡ ✡ ✡ � ✁ ✞ ✂ ✡ ✞ ✞ ✂ ✟ ☛ ✡ ✡ ✡ ✟ ☞ ✂ ☛ � ✠ ✡ ☞ ☞ � ✠ � ✁ ✂ ✝ ✁ ☞✌ ✡ ☛ ✂ ✄ ✁ ✂ ✟ ✟ ✂ ✞ ✄ � ✁ ✂ ✄ ✡ Gaussian Channel Capacity Shannon, 1948 : The capacity of a noisy channel with signal-to-noise ratio and bandwidth in Hz is given by bits/sec ✆✞✝ Example: Telephone channel has dB ✂✆☎ ( ) and Hz. Thus ✁ ✆☎ bits/sec ✡ ✠✟ ✆✞✝ Data Networks, Physical Layer, c 1996–2005, P . Mathys – p.6/37
� Gaussian Channel Capacity Capacity C/W = log 2 (1+S/N) of Gaussian Channel 18 16 14 12 C/W [bits/sec/Hz] 10 8 6 4 2 0 −10 0 10 20 30 40 50 S/N [dB] Data Networks, Physical Layer, c 1996–2005, P . Mathys – p.7/37
☛ ✡ ☎ ✡ � � � ✡ ✡ ✡ ☎ � � ✞ ☎ Guided Transmission Media Magnetic media. Twisted pair wire. UTP (unshielded twisted pair): CAT 3 (16 MHz BW), CAT 5 (100 MHz BW), CAT 6 (250 HMz BW), CAT 7 (600 MHz BW). Coaxial cable. 50-ohm, 75-ohm. Bandwidth GHz. Step-index multimode (“multimode”) optical fiber. 62.5/125 m (core/cladding) or 50/125 m are common ( m at 1 Gb/s, using 1300 nm LED). Graded-index multimode (“laser optimized”) optical fiber. 50/125 m ( m at 10 Gb/s, using 850 nm laser). Single-index monomode (“single-mode”) optical fiber. 8.3 m core (up to 40 km at 10 Gb/s, using 1550 nm laser). Data Networks, Physical Layer, c 1996–2005, P . Mathys – p.8/37
� Optical Fiber Types Data Networks, Physical Layer, c 1996–2005, P . Mathys – p.9/37
� Optical Fibers Data Networks, Physical Layer, c 1996–2005, P . Mathys – p.10/37
� Why Different Fibers? The costs associated with single-mode systems are about 25–30% higher than multimode systems operated at the same speed. Long wavelength (1310 nm, 1550 nm) electronics are more expensive. Single mode fiber requires significantly tighter alignment tolerances to couple light into its tiny core, necessitating transceivers and connector using high precision mechanics. Data Networks, Physical Layer, c 1996–2005, P . Mathys – p.11/37
✁ ✁ ✁ � � � � � ✁ � Optical Fiber Types Attenuation Fiber Type m MHz km MHz km dB/km dB/km 850 nm 1300 nm 850 nm 1300 nm Multimode Standard 62.5/125 m 62.5 200 500 3.5 1.0 Standard 50/125 m 50 500 500 3.5 1.5 Laser-Opt 50/125 m 50 1500 500 3.5 1.5 Attenuation Fiber Type m MHz km MHz km dB/km dB/km 850 nm 1300 nm 1310 nm 1550 nm Single-Mode Standard SMF 8.2 n/a n/a 0.4 0.3 Data Networks, Physical Layer, c 1996–2005, P . Mathys – p.12/37
� Optical Fiber IR Attenuation Data Networks, Physical Layer, c 1996–2005, P . Mathys – p.13/37
� � � � � � � � Ethernet Wiring Standard Year Rate Topo Medium Max Len 10Base5 1983 10 Mb/s Bus 50 Thick Coax 500 m 10Base2 1985 10 Mb/s Bus 50 Thin Coax 185 m 10BaseT 1990 10 Mb/s Star 100 Cat.3 UTP 100 m 100BaseTX 1995 100 Mb/s Star 100 Cat.5 UTP 100 m 100BaseFX 1995 100 Mb/s Star 2 optical fibers 2000 m 100BaseT4 1995 100 Mb/s Star 100 Cat.3 UTP 100 m 100BaseT2 1997 100 Mb/s Star 100 Cat.3 UTP 100 m 1000BaseLX 1998 1 Gb/s Star Multi-mode fiber 550 m 1000BaseLX 1998 1 Gb/s Star Single-mode fiber 5000 m 1000BaseT 1999 1 Gb/s Star 100 Cat.5 UTP 100 m 10GBaseLX4 2002 10 Gb/s Star MMF 1310 nm WDM 300 m 10GBaseLX4 2002 10 Gb/s Star SMF 1310 nm WDM 10 km 10GBaseSR 2002 10 Gb/s Star MMF 850 nm 26-300 m 10GBaseEW 2002 10 Gb/s Star SMF 1550 nm 40 km Data Networks, Physical Layer, c 1996–2005, P . Mathys – p.14/37
� Media Independent Interface Data Networks, Physical Layer, c 1996–2005, P . Mathys – p.15/37
� Ethernet Wiring Standard Cable Data Rate Coding Baud Rate Traffic 10BaseT 2p Cat.3 UTP 10 Mb/s Manch. 10 Mbd Full-Dup 100BaseTX 2p Cat.5 UTP 100 Mb/s 4B/5B 125 Mbd Full-Dup 100BaseFX 2 fibers 100 Mb/s 4B/5B 125 Mbd Full-Dup 100BaseT4 4p Cat.3 UTP 100 Mb/s 8B6T 25 Mbd Half-Dup 100BaseT2 4p Cat.3 UTP 100 Mb/s PAM5x5 25 Mbd Full-Dup 1000BaseLX 2 MMF/SMF 1 Gb/s 8B/10B 1.25 Gbd Full-Dup 1000BaseT 4p Cat.5 UTP 1 Gb/s 4D-PAM5 125 Mbd Full-Dup 10GBaseLX4 MM/SM 4WDM 10 Gb/s 8B/10B 3.125 Gbd Full-Dup 10GBaseSR 2 MMF/SMF 10 Gb/s 64B/66B 10.3 Gbd Full-Dup Data Networks, Physical Layer, c 1996–2005, P . Mathys – p.16/37
✡ ✡ ✞ ✞ ✠ ✞ ✞ ✡ ✡ ✡ ✡ ✞ ✞ ✡ ✞ ✞ ✡ ✡ ✡ ✡ ✞ ✡ ✞ ✠ ✡ � ✞ ✡ ✡ ✞ ✡ ✡ ✞ ✡ ✡ ✡ ✡ ✡ ✞ ✡ ✞ ✞ ✡ ✡ ✡ ✠ Timing Extraction Suppose you need to transmit the message “I am a ...”. In ASCII (LSB first) this becomes The straightforward way to send this over a wire or fiber is to use NRZ (non-return to zero) encoding: Problem: Long runs of zeros and/or ones make it difficult to extract timing information at the receiver. Data Networks, Physical Layer, c 1996–2005, P . Mathys – p.17/37
☎ ✂ ☎ ☎ ✁ � ✄ � � ✂ ☎ ✁ ✂ � ✄ � ✂ Coding for Timing Extraction Manchester coding: 1 is low high and 0 is high low transition in middle of symbol interval. Doubles bandwidth required. Has no dc component. NRZI (NRZ inverted) coding: 1 is encoded as transition (alternating low high and high low), 0 is encoded as absence of transition. Only solves problem of consecutive 1’s. Runlength-limited coding: At least 0’s must follow each 1, at most 0’s in sequence. Together with NRZI encoding this ensures transitions are not too close together and not too far apart. ✂ ✄✂ Runlength-limited coding: At most consecutive 0’s and at most consecutive 1’s are allowed. Data Networks, Physical Layer, c 1996–2005, P . Mathys – p.18/37
� ✂ ✄ � ✂ ☛ ✄ � ✡ ✡ ✂ ✄ � ✄ ✂ ✌ ✄ � ✡ ✄ ✂ � � � ✁ ✄ ✄ ✄ ✁ � ✂ ✁ ✡ � ✄ ✡ ✂ � � ✡ Coding for Timing Extraction Bipolar or AMI (alternate mark inversion) coding: Uses three levels, 0 and . 0’s are coded as 0 level and 1’s are coded as alternating and . Has no dc component, but long strings of 0’s yield no timing information. BNZS (bipolar -zero substitution) coding: All strings of zeros are replaced with special symbol sequence containing at least one bipolar violation. Examples are , , . For substitutions are after or after Data Networks, Physical Layer, c 1996–2005, P . Mathys – p.19/37
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