The document discusses convolution codes. It defines convolution codes as having three parameters (n, k, m) where n is the number of output bits, k is the number of input bits, and m is the number of memory registers. Convolutional codes add redundancy to protect data sent over noisy channels and are characterized by their constraint length L, which represents the number of bits in the encoder memory affecting output. The document provides an example of a (2,1,4) convolutional code and illustrates its operation through input sequences, state diagrams, tree diagrams, and trellis diagrams. It also describes methods for decoding convolution codes including sequential decoding using the Fano algorithm and maximum likelihood decoding using the Viterbi algorithm.
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.
BCH codes, part of the cyclic codes, are very powerful error correcting codes widely used in the information coding techniques. This presentation explains these codes with an example.
Convolution codes - Coding/Decoding Tree codes and Trellis codes for multiple...Madhumita Tamhane
In contrast to block codes, Convolution coding scheme has an information frame together with previous m information frames encoded into a single code word frame, hence coupling successive code word frames. Convolution codes are most important Tree codes that satisfy certain additional linearity and time invariance properties. Decoding procedure is mainly devoted to correcting errors in first frame. The effect of these information symbols on subsequent code word frames can be computed and subtracted from subsequent code word frames. Hence in spite of infinitely long code words, computations can be arranged so that the effect of earlier frames, properly decoded, on the current frame is zero.
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.
BCH codes, part of the cyclic codes, are very powerful error correcting codes widely used in the information coding techniques. This presentation explains these codes with an example.
Convolution codes - Coding/Decoding Tree codes and Trellis codes for multiple...Madhumita Tamhane
In contrast to block codes, Convolution coding scheme has an information frame together with previous m information frames encoded into a single code word frame, hence coupling successive code word frames. Convolution codes are most important Tree codes that satisfy certain additional linearity and time invariance properties. Decoding procedure is mainly devoted to correcting errors in first frame. The effect of these information symbols on subsequent code word frames can be computed and subtracted from subsequent code word frames. Hence in spite of infinitely long code words, computations can be arranged so that the effect of earlier frames, properly decoded, on the current frame is zero.
pull up to pull down ratio of nmos inverter driven by another nmos inverter and also another describing with pass transistor. Transistor sizing with example and some formulas
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
Base band transmission
*Wave form representation of binary digits
*PCM, DPCM, DM, ADM systems
*Detection of signals in Gaussian noise
*Matched filter - Application of matched filter
*Error probability performance of binary signaling
*Multilevel base band transmission
*Inter symbol interference
*Eye pattern
*Companding
*A law and μ law
*Correlation receiver
Manchester & Differential Manchester encoding schemeArunabha Saha
The two main variants of biphase encoding techniques are discussed here. Manchester and Differential Manchester encoding scheme are explained with examples. Comparison between several classes of polar encoding techniques are done along with the exposure about the advantages and disadvantages of both schemes.
Digital Data, Digital Signal | Scrambling TechniquesBiplap Bhattarai
Digital signal is a sequence of discrete, discontinuous voltage pulses.
Each pulse is a signal element.
Binary data are transmitted by encoding the bit stream into signal elements.
In the simplest case, one bit is represented by one signal element.
- E.g., 1 is represented by a lower voltage level, and 0 is represented by a higher voltage level
Introduction to Convolutional Codes
Convolutional Encoder Structure
Convolutional Encoder Representation(Vector, Polynomial, State Diagram and Trellis Representations )
Maximum Likelihood Decoder
Viterbi Algorithm
MATLAB Simulation
Hard and Soft Decisions
Bit Error Rate Tradeoff
Consumed Time Tradeoff
Analysis and Implementation of Hard-Decision Viterbi Decoding In Wireless Com...IJERA Editor
Convolutional codes are also known as Turbo codes because of their error correction capability. These codes are
also awarded as Super product codes, because these codes have replaced the backward error correction codes.
Turbo codes are much more efficient than previous backward error correction codes because these are Forward
error correction (FEC) codes and there is no need for a feedback link to request the transmitter for
retransmission of data, when bits are corrupted in the information channel. A Viterbi decoder decodes stream of
digital data bits that has been encoded by Convolutional encoder. In this paper we introduce a RSC (Recursive
Systematic Convolutional) encoder with constraint length of 2 code rate of 1/3. The RSC encoder and Viterbi
decoder both are implemented on paper, as well as in MATLAB. Simulation results are also presented by using
MATLAB.
pull up to pull down ratio of nmos inverter driven by another nmos inverter and also another describing with pass transistor. Transistor sizing with example and some formulas
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
Base band transmission
*Wave form representation of binary digits
*PCM, DPCM, DM, ADM systems
*Detection of signals in Gaussian noise
*Matched filter - Application of matched filter
*Error probability performance of binary signaling
*Multilevel base band transmission
*Inter symbol interference
*Eye pattern
*Companding
*A law and μ law
*Correlation receiver
Manchester & Differential Manchester encoding schemeArunabha Saha
The two main variants of biphase encoding techniques are discussed here. Manchester and Differential Manchester encoding scheme are explained with examples. Comparison between several classes of polar encoding techniques are done along with the exposure about the advantages and disadvantages of both schemes.
Digital Data, Digital Signal | Scrambling TechniquesBiplap Bhattarai
Digital signal is a sequence of discrete, discontinuous voltage pulses.
Each pulse is a signal element.
Binary data are transmitted by encoding the bit stream into signal elements.
In the simplest case, one bit is represented by one signal element.
- E.g., 1 is represented by a lower voltage level, and 0 is represented by a higher voltage level
Introduction to Convolutional Codes
Convolutional Encoder Structure
Convolutional Encoder Representation(Vector, Polynomial, State Diagram and Trellis Representations )
Maximum Likelihood Decoder
Viterbi Algorithm
MATLAB Simulation
Hard and Soft Decisions
Bit Error Rate Tradeoff
Consumed Time Tradeoff
Analysis and Implementation of Hard-Decision Viterbi Decoding In Wireless Com...IJERA Editor
Convolutional codes are also known as Turbo codes because of their error correction capability. These codes are
also awarded as Super product codes, because these codes have replaced the backward error correction codes.
Turbo codes are much more efficient than previous backward error correction codes because these are Forward
error correction (FEC) codes and there is no need for a feedback link to request the transmitter for
retransmission of data, when bits are corrupted in the information channel. A Viterbi decoder decodes stream of
digital data bits that has been encoded by Convolutional encoder. In this paper we introduce a RSC (Recursive
Systematic Convolutional) encoder with constraint length of 2 code rate of 1/3. The RSC encoder and Viterbi
decoder both are implemented on paper, as well as in MATLAB. Simulation results are also presented by using
MATLAB.
Hard Decision Viterbi Decoder: Implementation on FPGA and Comparison of Resou...IJERA Editor
Viterbi decoder is the most important part in receiver section of wireless communication system. Viterbi
algorithm is one of the most common decoding algorithms used for decoding convolutional codes. Viterbi
decoder employs Maximum Likelihood technique to decode the convolutionally encoded data stream. In
practice, most of the communication systems use Viterbi decoding scheme in processors. But increased interest
on high speed Viterbi decoder in a single chip forced to realize with the speed of Giga-bit per second, without
using memory or off-chip processors. Implementation of proposed design and realization is possible due to
advanced Field Programmable Gate Array (FPGA) technologies and advanced Electronic Design Automatic
(EDA) tools. This paper involves designing an optimum structure of Viterbi decoder and implementing it on
different FPGA devices to compare the resource utilizations.
Data Communication & Computer Networks:Digital Signal EncodingDr Rajiv Srivastava
These slides cover the fundamentals of data communication & networking. It covers Digital signal Encoding which are used in communication of data over transmission medium. it is useful for engineering students & also for the candidates who want to master data communication & computer networking.
International Journal of Computational Engineering Research(IJCER)ijceronline
International Journal of Computational Engineering Research (IJCER) is dedicated to protecting personal information and will make every reasonable effort to handle collected information appropriately. All information collected, as well as related requests, will be handled as carefully and efficiently as possible in accordance with IJCER standards for integrity and objectivity.
3. Codes (contd.)
1 Source Codes
• The aim of source coding is to take the
source data and make it smaller.
2 Channel Codes
• The aim of channel coding theory is to
find codes which transmit
quickly, contain many valid code words
and can correct or at least detect many
errors.
Pratishtha Shira Ram
4. Channel Codes
Channel codes are used to add redundancy to the codes.
Redundancy adds extra information about the data into the signal.
This extra information ensures that the data is received correctly at the
information sink.
Hence, channel codes increase the BER of the signal.
The aim of channel coding
The channel code is used to theory is to find codes which
protect data sent over it for transmit quickly, contain
storage or retrieval even in the many valid code words and
presence of noise (errors). can correct or at least detect
many errors.
Pratishtha Shira Ram
5. Convolution Codes
Convolutional codes are characterized by
thee parameters:
(n, k, m)
Where,
n= Number of output bits
k= Number of input bits
m= Number of memory registers
Code Rate = k/n
=Number of input bits
/Number of output bits
Constraint length “L”= k(m-1)
L represents the no. of bits in the encoder
memory that affects the generation of n
output bits
Pratishtha Shira Ram
6. An example: (2,1,4) Coder
n= Number of output bits 2
k= Number of input bits 1
m= Number of memory registers 4
Constraint length L=3
The no. of bits in the
shaded registers are called
states of code, and are
defined by
No. of states = 2L
Pratishtha Shira Ram
7. (2,1,4) Coder
The constraint length = 3.
The shaded registers hold these bits, while
the un-shaded register holds the incoming
bit.
This means, 3 bits, or 8 different
combinations of the bits can be held in the
registers.
These 8 combinations determine what
output will be received as the the 2 output
bits v1 and v2.
Pratishtha Shira Ram
8. Input sequence: 1,Output: 11 11 10 11
t=0; C
Input state
=000 t=2;
A
Input bit=1 Input state =010
Output bit=11 Input bit=0
Output bit=10
t=1;
B
Input state =100
Input bit=0
D
Output bit=11
t=3;
Input state =101
Input bit=0
Output bit=11
Pratishtha Shira Ram
9. The convolution
Providing input of 1 to the coder provides what is called the ”impulse response”
of that coder.
Here, providing 1 as input (and then „flushing‟ it out from the registers using
zeros) gave the output sequence : 11 11 10 11.
Similarly, response for input bit 0 would be : 00 00 00 00.
The output sequence can be computed simply by convolving the input sequence
u with the impulse response g.
Or,
v=u*g
By the principle of linear superposition, a coded sequence can be generated
from the impulse response.
Pratishtha Shira Ram
10. Example
To find the coded sequence for the input 1011, we just have to add the shifted
versions of the individual responses:
Input bit Its Impulse Response
1 11 11 10 11
0 00 00 00 00
1 11 11 10 11
1 11 11 10 11
1011 11 11 01 11 01 01 11
This result can be verified by the encoder model too.
Pratishtha Shira Ram
11. Output bits and the encoder bits through
the(2,1,4) code:
Pratishtha Shira Ram
13. Understanding the encoder design
There are three graphical ways in which the encoder can be understood better:
1. State diagram
2. Tree diagram
3. Trellis diagram
State Diagram
Pratishtha Shira Ram
17. Deconvolution of codes
There are 2 basic methods of deconvolution
1. Sequential decoding: Fano algorithm
- It allows both forward and backward movement through the Trellis diagram
flow.
-If instead of 11 11 01 11 01 01 11, the code 01 11 01 11 01 01 11 is
received, the algorithm will take a start and tally with the outputs it finds on the
way. If an output does not tally, it retraces its position back to the previous
ambiguous decision.
2. Maximum –Likelihood decoding: Viterbi algorithm
-The viterbi decoder examines the entire received sequence of a given length.
-The decoder then computes a metric for the path and then makes a decision
based on it.
-The path with the higher metric is kept, and the one with the lower one is
discarded.
- Generally the Hamming distance is used as the metric here.
Pratishtha Shira Ram