Exam 10: Channel Coding

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An IR remote control sends a 25-bit sequence every 0.01 s.The data rate of this remote control equals _______ bps.

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 2500. 25 bits /0.01 s=2,500bps\text { 2500. } 25 \text { bits } / 0.01 \mathrm {~s} = 2,500 \mathrm { bps }

Adding a parity bit to a data byte results in a DIF == (x/y)( x / y ) .

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The channel from a space probe to earth has a bandwidth B=106B = 10 ^ { 6 } Hz.The channel capacity when the probe is 10310 ^ { 3 } km from earth is C=107C = 10 ^ { 7 } bps = 10 Mbps.Using the inverse square law to describe the signal power loss, the capacity when the probe is at 2×1032 \times 10 ^ { 3 } km from earth equals _____ Mbps.Assume that the noise power is constant.

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log2(1+σs2(αro)/σN2)=C/B=10σs2(αro)/σN2=1023. At 2r0,σs2(αro)/σN2=1023/4=255.75\log _ { 2 } \left( 1 + \sigma _ { s } ^ { 2 } \left( \alpha r _ { o } \right) / \sigma _ { N } { } ^ { 2 } \right) = C / B = 10 \rightarrow \sigma _ { s } { } ^ { 2 } \left( \alpha r _ { o } \right) / \sigma _ { N } { } ^ { 2 } = 1023 . \text { At } 2 r _ { 0 } , \sigma _ { s } { } ^ { 2 } \left( \alpha r _ { o } \right) / \sigma _ { N } { } ^ { 2 } = 1023 / 4 = 255.75 log2(255.75+1)=8C=8B=8Mbps\rightarrow \log _ { 2 } ( 255.75 + 1 ) = 8 \rightarrow C = 8 B = 8 \mathrm { Mbps }

Consider the binary data packet shown as a spreadsheet with columns indicated by letters and rows by numbers.The last row contains the LRC and there is one error.The letter-number address of the error is___. A B C D E 1 1 1 0 0 1 2 0 1 0 1 1 3 0 0 1 0 1 4 1 1 1 1 1 5 1 0 0 1 1

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The SNR of the channel from a space probe to earth equals 2047 and the channel capacity C = 5 x 10710 ^ { 7 } bps.The channel bandwidth = _________ (x.xx) MHz.

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The threshold intensity for a receiver Ir=2.5×106 W/m2\mathrm { I } _ { \mathrm { r } } = 2.5 \times 10 ^ { - 6 } \mathrm {~W} / \mathrm { m } ^ { 2 } If the intensity produced by an antenna equals 10 W/m210 \mathrm {~W} / \mathrm { m } ^ { 2 } at a range of 1 m, the maximum reliable range of the system equals ____ km.

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An error-correction scheme appends a parity bit to each data byte to form code word and the sequence of 15 code words is followed by a longitudinal redundancy check (LRC) code word to orm a data packet.The resulting DIF = ____ .

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The channel from a space probe to earth has a bandwidth B=106B = 10 ^ { 6 } Hz and a channel capacity C = 0.8×107 bps 0.8 \times 10 ^ { 7 } \text { bps } .The signal-to-noise ratio σs2/σN2\sigma _ { s } { } ^ { 2 } / \sigma _ { N } { } ^ { 2 } equals ______.

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Consider the binary data packet shown as a spreadsheet with columns indicated by letters and rows by numbers.The parity bits are in column E.The code words use _____ parity and the LRC uses _____ parity. A B C D E 1 0 1 0 0 1 2 0 1 1 1 1 3 0 0 1 0 1 4 1 1 1 1 0 5 0 0 0 1 1

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A movie source generates a set of 1080p HD digital image files, each file composed of 1920 x 1080 picture elements (pixels), with each pixel specified with three bytes of information.When the source produces 30 images per second, its raw (uncoded) data rate equals _____ (x.xx10γ)\left( x . x x 10 ^ { \gamma } \right) bps.

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The data rate produced by a typist is 56 bits/second.Assuming that the text is encoded using the standard 8-bit ASCII code, the number of letters that is typed in one second equals ____ letters/second.

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