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Channel Capacity

Channel Capacity, C is defined as
‘the maximum mutual information I(X; Y) in any single use of
the channel, where the maximization is over all possible input
probability distributions {p(xj)} on X”
C is measured in bits/channel-use, or bits/transmission.

Information Capacity Theorem:- is defined as
‘The information capacity of a continuous channel of bandwidth B
hertz, perturbed by additive white Gaussian noise of power spectral
density
N0/2
and limited in bandwidth to B, is given by
C = B log2(1 +P/N0B)
where P is the average transmitted power.

Assumptions:
1. band-limited, power-limited Gaussian channels.
2. A zero-mean stationary process X(t) that is band-limited to Bhertz, sampled at Nyquist rate of 2B samples per second
3. These samples are transmitted in T seconds over a noisy
channel, also band-limited to B hertz.
The number of samples, K is given by
K = 2BT

Encryption

Encryption:-The translation of data into a secret code. Encryption is the most effective way to achieve data security.
Encryption is the process of converting information into
an encrypted form, so that it is intelligible only to
someone who knows how to decrypt it to obtain the
original message.
Symmetric encryption:-A type of encryption where the same key is used to encrypt and decrypt the message.
public-key encryption:-
A cryptographic system that uses two keys -- a public key known to everyone and a private or secret key known only to the recipient of the message. An important element to the public key system is that the public and private keys are related in such a way that only the public key can be used to encrypt messages and only the corresponding private key can be used to decrypt them.

Advantages of Digital Communication

Digital Communication advantages
*Reliable communication; less sensitivity to changes in environmental conditions (temperature, etc.)
*Easy multiplexing
*Easy signaling
*In digital communications Hardware implementation is flexible with the use of microprocessors and large scale integrated circuits.
*As channel coding is used in Digital Communication the errors in transmission may be detected and corrected in Receivers.
*Hook status, address digits, call progress information
*Voice and data integration
*Easy processing like encryption and compression
*Easy system performance monitoring
*QOS monitoring
*Integration of transmission and switching
*Signal regeneration, operation at low SNR, superior performance

Digital vs Analog Signal Transmission

Digital transmission has several advantages over Analog transmission:
1. Analog circuits require amplifiers, and each amplifier adds distortion and noise to the
signal.
2. In contrast, digital amplifier regenerate an exact signal, eliminating cumulative
errors.An incoming (analog) signal is sampled,
then generates a new signal from the bit value; the incoming signal is discarded.
3.)Voice, data, video, etc. can all by carried by digital circuits.
With analog circuits, intermediate nodes amplify the incomiing signal, noise and all.
4.)Digital Communication systems are cheaper to implement then analog.
5.)Digital signals can be coded to yield extremely low error rates and high fidelity as well as privacy.
6.)Easier and more efficient to multiplex several digital signals.such as speech,video and other digital data.
7.)Digital Communication is inherently more efficient than analog in realizing the exchange of signal to noise ration for Band width.
8.)In digital communications Hardware implementation is flexible with the use of microprocessors and large scale integrated circuits.