Mathematical Explanation of channel capacityHere we can see that the channel capacity is measured with the multiplication of pulses per second and information. This is how we can measure the channel capacity.
A Brief Knowledge about Differential Pulse Code Modulation.
It contains the basics of Pulse Code modulation and why we all switching to Differential Pulse Code Modulation.
All the things about the Differential Pulse Code Modulation is given in a good understandable way
It is a digital representation of an analog signal that takes samples of the amplitude of the analog signal at regular intervals. The sampled analog data is changed to, and then represented by, binary data.
Here we study the channel capacity of the signal from analog and digital communication signals. Also study data rates limit , Noisy-channel coding theorem, Shannon capacity theorem.
The Presentation is as per the syllabus of the subject ”Digital Communication” of B.E. VIth Semester of Sant Gadge Baba Amravati University, Maharashtra, India
Contents are
Digital Communication System
Line Coding
Scrambling
A Brief Knowledge about Differential Pulse Code Modulation.
It contains the basics of Pulse Code modulation and why we all switching to Differential Pulse Code Modulation.
All the things about the Differential Pulse Code Modulation is given in a good understandable way
It is a digital representation of an analog signal that takes samples of the amplitude of the analog signal at regular intervals. The sampled analog data is changed to, and then represented by, binary data.
Here we study the channel capacity of the signal from analog and digital communication signals. Also study data rates limit , Noisy-channel coding theorem, Shannon capacity theorem.
The Presentation is as per the syllabus of the subject ”Digital Communication” of B.E. VIth Semester of Sant Gadge Baba Amravati University, Maharashtra, India
Contents are
Digital Communication System
Line Coding
Scrambling
Hello everyone. This is a short presentation on path loss and shadowing. I have not covered all the topics but a brief idea is given on path loss and wireless channel propagation models.
Hope you find it useful.
Thanks
Objective of Pulse Code Modulation
Block Diagram of PCM
Process of PCM
Sampling
Quantization
Encoding
PCM Standards
Bit Rate and Bandwidth in PCM
Advantages and Disadvantages of PCM
Applications of PCM
A second important technique in error-control coding is that of convolutional coding . In this type of coding the encoder output is not in block form, but is in the form of an encoded
sequence generated from an input information sequence.
convolutional encoding is designed so that its decoding can be performed in some structured and simplified way. One of the design assumptions that simplifies decoding
is linearity of the code. For this reason, linear convolutional codes are preferred. The source alphabet is taken from a finite field or Galois field GF(q).
Convolution coding is a popular error-correcting coding method used in digital communications.
The convolution operation encodes some redundant information into the transmitted signal, thereby improving the data capacity of the channel.
Convolution Encoding with Viterbi decoding is a powerful FEC technique that is particularly suited to a channel in which the transmitted signal is corrupted mainly by AWGN.
It is simple and has good performance with low implementation cost.
Sampling is a Simple method to convert analog signal into discrete Signal by using any one of its three methods
if the sampling frequency is twice or greater than twice then sampled signal can be convert back into analog signal easily......
Hello everyone. This is a short presentation on path loss and shadowing. I have not covered all the topics but a brief idea is given on path loss and wireless channel propagation models.
Hope you find it useful.
Thanks
Objective of Pulse Code Modulation
Block Diagram of PCM
Process of PCM
Sampling
Quantization
Encoding
PCM Standards
Bit Rate and Bandwidth in PCM
Advantages and Disadvantages of PCM
Applications of PCM
A second important technique in error-control coding is that of convolutional coding . In this type of coding the encoder output is not in block form, but is in the form of an encoded
sequence generated from an input information sequence.
convolutional encoding is designed so that its decoding can be performed in some structured and simplified way. One of the design assumptions that simplifies decoding
is linearity of the code. For this reason, linear convolutional codes are preferred. The source alphabet is taken from a finite field or Galois field GF(q).
Convolution coding is a popular error-correcting coding method used in digital communications.
The convolution operation encodes some redundant information into the transmitted signal, thereby improving the data capacity of the channel.
Convolution Encoding with Viterbi decoding is a powerful FEC technique that is particularly suited to a channel in which the transmitted signal is corrupted mainly by AWGN.
It is simple and has good performance with low implementation cost.
Sampling is a Simple method to convert analog signal into discrete Signal by using any one of its three methods
if the sampling frequency is twice or greater than twice then sampled signal can be convert back into analog signal easily......
Sampling Theorem, Quantization Noise and its types, PCM, Channel Capacity, Ny...Waqas Afzal
Sampling Theorem
Quantization
Noise and its types
Encoding-PCM
Power of Signal
Signal to noise Ratio
Channel Capacity
Nyquist Bandwidth
Shannon Capacity Formula
Multirate Digital Signal Processing-Up/Down Sampling
Applications
In this we discuss about DATA RATE LIMITS
Two theoretical formulas were developed to calculate the data rate:
Nyquist bit rate for a noiseless channel
BitRate = 2 * bandwidth * log 2 L
2: Shannon Capacity for a noisy channel
Capacity = bandwidth * log 2 (1 + SNR)
...............
PERFORMANCE (Network PERFORMANCE) :
Bandwidth: ( Bandwidth in Hertz and Bandwidth in Bits per Seconds) :
Throughput:
These above topics covered in this slide
Thanks You!
Data and Computer Communications ,Transmission Terminology Frequency Domain Concepts Advantages & Disadvantages of Digital Signals Audio Signals Video Signals Analog and Digital Transmission ATTENUATION Noise
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2. INTODUCTION
• Channel capacity, in Electrical engineering, Computer
science, and Information theory, is the tight upper
bound on the rate at which information can be reliably
transmitted over a communication channel .
• The channel capacity of a given channel is the highest
information rate (in units of information per unit time) that
can be achieved with arbitrarily small error probability.
• Bandwidth and noise power place a restriction upon the
rate of information through a channel for low error
transmission. The highest bit rate achievable for no
error transmission is termed as the channel capacity.
3. COMMUNICATION -
• According to Merriam Webster process by which
information is exchanged between individuals
through a common system of symbols, signs, or
behavior.
• DIGITAL COMMUNICATION –
Digital communications is any exchange of data
that transmits the data in a digital form. For
example, communications done over
the Internet is a form of digital communication.
4. • According to Cambridge dictionary
to direct something into a particular place
or situation is called a channel. Following are list of
some of the forms of communication with channels
of disseminating information. This are,
• i) Oral
• ii) Documentary
• iii) Audio - Visual
5. BIT RATE -
• Bit rate, as the name implies, describes the rate at which bits are
transferred from one location to another. In other words, it measures how
much data is transmitted in a given amount of time. Bit rate is commonly
measured in bits per second (bps), kilobits per second (Kbps), or megabits
per second (Mbps).
BANDWIDTH –
Bandwidth describes the maximum data transfer rate of
a network or Internet connection. It measures how much data can
be sent over a specific connection in a given amount of time. For
example, a gigabit Ethernet connection has a bandwidth of
1,000 Mbps. An Internet connection via cable modem may provide
25 Mbps of bandwidth.
7. The components of the information model of C.E .
Shannon is explained here :
•Information Source: An ensemble of messages from
which selections are made for transmission.
•Encoder : Encodes a message to a signal There will be
one to one correspondence between the message alphabet
and the signal, therefore, there will be no ambiguity in
the encoding process
•Channel : Band of frequencies within which signals must be
kept
•Decoder : Decodes a message from a signal.
•Noise : Received signal is not the one transmitted.
8. Mathematical Explanation of channel capacity:
If a source gives M equally likely message M >>1, With rate
of information R and given channel with capacity C.
Then if
R <=C In this condition error free transmission is possible
in presence of noise
If
R > c In this conditions probability of error is close to
unity or equal to 1.
9. Shannon Hartley channel capacity formula :
Here
• C - Channel capacity in bits per sec
• B - Bandwidth of the channel in hertz
• S - Average signal power over the bandwidth (watt)
• N - Average power of the noise and interference over the
bandwidth (watts)
• S/N – Signal to Noise Ratio (SNR) or carrier – to – noise
ratio (CNR)
• Here one can receive a signal with noise in every session.
Because of noise is there at the channel we receive signal
and noise both together.
10. Noiseless Channels and Nyquist
Theorem
• For a noiseless channel, Nyquist theorem gives the relationship
• between the channel bandwidth and maximum data rate that can be
transmitted over this channel.
Nyquist Theorem
mBC 2log2
C: channel capacity (bps)
B: RF bandwidth
m: number of finite states in a symbol of transmitted signal
11. So we receive
Signal = Signal power (S) + Noise Power (N)
And its mean square value is
Where S = signal power
N = Noise power and
Root ( ) means square value of signal is ,
So noise power is N and its mean square value is .
So if we want to identify number of levels will be separated
without error is
m = Ratio of Signal / Noise signal
m =
12. m - Here levels of signals without error ,
is denoted as received signal with error and is noise signal.
So here the signal without error is
>
So digital information is -
I = log2 m
= log 2
= ½ log2
Here I is digital information
m is the signal without error and it is
So the channel signal is ½ log 2
13. Now if a channel transmits K pulses per second
then channel capacity is
C = IK (Information multiplied with pulses)
= K/2 log2 ( 1+S/N)
• From Nyquist theorem we know that k=2B, then we
get the value of channel capacity C,
14. Conclusion -
Here we can see that the channel capacity is
measured with the multiplication of pulses
per second and information. This is how we
can measure the channel capacity.
Though Shannon’s theory was presented
with regard to the problem of transmitting
error- free messages across telephone lines,
this theory is being used in such fields as ,
psychology, education , managmen decision
process and information science. Because of its
generality, this theory became known as
information theory.