CCS

Channel Capacity and Coding

The objective of any communication system is to transmit information generated by an
information source from one location to another. The medium over which information
is transmitted is called the communication channel. We have already seen
that the information content of a source is measured by the entropy of the source, and
the most common unit for this quantity is bits. We have also seen that an appropriate
mathematical model for an information source is a random process.

Channel Model and Channel Capacity

A communication channel transmits the information-bearing signal to the destination.
In this transmission, the information-carrying signal is subject to a variety of changes.
Some of these changes are deterministic in nature-for example, attenuation and linear
and nonlinear distortion-and some are probabilistic-for example, addition of noise,
multipath fading, and so on. Because deterministic changes can be considered as special
cases of random changes, in the most general sense the mathematical model for a

communication channel is a stochastic dependence between the input and the output
signals.

Channel Model

Channel Capacity

Matlab Coding

 1  % MATLAB script for Illustrative Problem 10.1.
 2 echo on
 3 gamma_db=[-20:0.1:20];
 4 gamma=10.^(gamma_db./10);
 5 p_error=q(sqrt(2.*gamma));                       # equation 10.2.8
 6 capacity=1.-entropy2(p_error);                   # equation 10.2.3
 7 pause % Press a key to see a plot of error probability vs. SNR/bit.
 8 clf
 9 semilogx(gamma,p_error)
10 xlabel('SNR/bit')
11 title('Error probability versus SNR/bit')
12 ylabel('Error Prob.')
13 pause % Press a key to see a plot of channel capacity vs. SNR/bit.
14 clf
15 semilogx(gamma,capacity)
16 xlabel('SNR/bit')
17 title('Channel capacity versus SNR/bit')
18 ylabel('Channel capacity')


Simulation Result

 a plot of error probability vs. SNR/bit

 a plot of channel capacity vs. SNR/bit

Reference,

　　1. <<Contemporary Communication System using MATLAB>> - John G. Proakis