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 bandwidth

limited channel  in the presence of noise

SHANNON’S LAW

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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 log2 (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!

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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 log10 1000/20 = 16.9897 dB

If the SNR is 20 dB, and the bandwidth available is 4 kHz, which is appropriate for telephone

communications, then C = 4 log2(1 + 100) = 4 log2 (101) = 26.63 kbit/s. Note that the value of 100 is

appropriate for an SNR of 20 dB.

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 = 0.035 corresponding to an SNR of -14.5 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

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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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