Information Capacity and
Communication Systems
By :
Mr. Gaurav Verma
Asst. Prof.
ECE Dept.
NIEC
SHANNON’S LAW
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 Theorem
(Shannon’s Limit for Information Capacity)

Claude Shannon at Bell Labs figured out how much information
a channel could theoretically carry:
Note that the log
I = B log2 (1 + S/N)
is base 2!



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)
3
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
4
Example
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.
Communication systems
Digital
Analog

The block diagram on the top shows the blocks common to all communication
7
systems
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
8
9