ECE4334-Session-2-Channel_Capacity

ECE4334-Session-2-Channel_Capacity - ECE4235 8/20/2009...

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ECE4235 8/20/2009 Prof. Dr. Othman O. Khalifa 2009 ١ Prof. Dr. Othman O. Khalifa © 2009 Lecturer: Prof. Dr. Othman O. Khalifa Office: Room 3.205 Phone: ex. 4528 Email: khalifa@iiu.edu.my ECE4334 Information Theory and Coding Session-2 Channel Capacity Review Sample Quantize Source Encode Encryption Channel Encoder Modulator Channel D/A Conversion Decryption Source Decoder Channel Decoder Equalizer Demodulator Analog Input signal Analog Output signal Digital Output Direct Digital Input This is the part of the system diagram that we are covering.
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ECE4235 8/20/2009 Prof. Dr. Othman O. Khalifa 2009 ٢ Prof. Dr. Othman O. Khalifa © 2009 Brief Introduction to Information Theory ) ; ( max ) ( Y X I C x p = Encoder Channel ) | ( x y p Decoder Message Estimate of Message W n X n Y W ˆ n X Is a codeword from an alphbet of size n (ex. A point in an 8 PSK consellation ) Channel capacity is the highest rate in bits per channel use at which information can be sent with arbitrary low probability of error. 3 Channel Capacity ± Capacity in the channel is defined as a intrinsic ability of a channel to convey information ± Using mutual information the channel capacity of a discrete memoryless channel is a maximum average mutual information in any single use of channel over all possible probability distributions
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ECE4235 8/20/2009 Prof. Dr. Othman O. Khalifa 2009 ٣ Prof. Dr. Othman O. Khalifa © 2009 A Little Information Theory Capacity for the Gaussian Channel () ( ) Y X I P X x p C ; E : max 2 = X Y Z + For a Gaussian Channel with Bandwidth, W + = W SNR W C 1 log 0 N P SNR = : bits per second 4 Example: binary symmetric channel (BSC) Error Source + E X Output Input E X Y = E is the binary error sequence s.t. P(1) = 1-P(0) = p X is the binary information sequence Y is the binary output sequence 1-p 00 p 11 1-p
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ECE4235 8/20/2009 Prof. Dr. Othman O. Khalifa 2009 ٤ Prof. Dr. Othman O. Khalifa © 2009 Channel Capacity ± Is the maximum rate at which data can be transmitted over a given channel ± There are four concepts that are interrelated: ¾ data rate (in bps) ¾ bandwidth of the transmitted signal (in Hz) ¾ noise (average level of noise over the channel/path) ¾ error rate ± Problem: how to maximize data rate for a given bw, noise and tolerable error rate? ± First consider a channel that is “noise free” ¾ limitation on data rate is the available bw for the signal • Nyquist: if signal transmission rate is 2B, then a signal with frequencies no greater than B is sufficient to carry the signal rate; or given a BW of B, the highest signal rate that can be carried is 2B 9 (limited by intersymbol interference, ISI) ¾ For binary signals (with two voltage levels): • B Hz supports 2B bps. ; For multiple M levels, C= 2B log_2 M ¾ doubling BW doubles data rate Channel Capacity ± Let us now consider the effect of noise ¾ noise causes signal degradation, bit error ¾ for a signal signal noise, greater signal strength improves the data reception (decreases BER) ¾ SNR measured at the RX (in dB) = 10 log_10 signal/noise ¾ SNR sets an upper bound on the achievable data rate
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ECE4334-Session-2-Channel_Capacity - ECE4235 8/20/2009...

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