Information Capacity and Communication Systems By : Mr. Gaurav Verma Asst. Prof. ECE Dept. NIEC

Shannon's law is any statement defining the theoretical maximum rate at which error free digits can be transmitted over a bandwidtherror limited channel in the presence of noise SHANNON’S LAW

3  Shannon’s Theorem (Shannon’s Limit for Information Capacity) Claude Shannon at Bell Labs figured out how much information a channel could theoretically carry: I = B log 2 (1 + S/N)  Where I is Information Capacity in bits per second (bps)  B is the channel bandwidth in Hz  S/N is Signal-to-Noise ratio (SNR: unitless…don’t make into decibel: dB) Note that the log is base 2!

4 Signal-to-Noise Ratio S/N is normally measured in dB (decibel). It is a relationship between the signal we want versus the noise that we do not want, which is in the medium. It can be thought of as a fractional relationship (that is, before we take the logarithm): 1000W of signal power versus 20W of noise power is either:  1000/20=50 (unitless!)  or: about 17 dB ==> 10 log /20 = dB

If the SNR is 20 dB, and the bandwidth available is 4 kHz, which is appropriate for telephone communications, then C = 4 log2( ) = 4 log2 (101) = kbit/s. Note that the value of 100 is appropriate for an SNR of 20 dB.SNR Example

If it is required to transmit at 50 kbit/s, and a bandwidth of 1 MHz is used, then the minimum SNR required is given by 50 = 1000 log2(1+S/N) so S/N = 2C/W -1 = corresponding to an SNR of dB. This shows that it is possible to transmit using signals which are actually much weaker than the background noise level. Example

7 The block diagram on the top shows the blocks common to all communication systems  Communication systems Digital Analog

8 We recall the components of a communication system: Input transducer: The device that converts a physical signal from source to an electrical, mechanical or electromagnetic signal more suitable for communicating Transmitter: The device that sends the transduced signal Transmission channel: The physical medium on which the signal is carried Receiver: The device that recovers the transmitted signal from the channel Output transducer: The device that converts the received signal back into a useful quantity

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