Presentation on error control coding techniques

1. ERROR CONTROL
CODING
TECHNIQUES
BY : DHANASHRI NANDRE
202081011
VJTI-ELECTRICAL DEPT. ELECTRONICS BRANCH- PRESENTATION FOR ACT
1

2. CONTENTS :
◦ Introduction & Explanation
- Need of error correcting codes.
- Cyclic Codes
- LDPC Codes
◦ Literature Survey
◦ Significance of previous research
◦ Performance Comparison
◦ Recommendation
◦ Future Scope
◦ Conclusion
◦ References
2

3. What is error ?
◦ The input data can’t be the same as the output data.This
mismatch is known as “Error”
◦ Result in the loss of important or secure data
◦ Types[1] -
1.Single Bit Errors
2.Multi Bit Errors
3.Burst Errors
3

4. What is Need Of Error Correcting Codes
◦ Requirements of communication systems
are stringent
◦ Reliability in communication increases
Cause of Error [1]-
Echo,crosstalk,impulsive noise,thermal
noise
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5. What is error Detection And Correction ?
Error Detection -
Detecting the errors which are present in the data transmitted
from transmitter to receiver[1]
Types of error detection-
● Parity Checking
● Cyclic Redundancy Check (CRC)
● Longitudinal Redundancy Check (LRC)
● Repetition codes
5

6. What is error Detection And Correction ?
Error Correction -
◦ After detecting the errors reconstructing the original error-
free data
◦ Ensures that corrected and error-free messages are obtained
at the receiver side
◦ Types of error detection[1]-
Automatic repeat request (ARQ)
Forward error correction
Hybrid schemes
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7. 7
Cyclic Codes

8. Cyclic Code
◦ Cyclic code is a linear code
◦ A linear [n,k] code C over a finite field GF(q) is called cyclic if
(C0,C1,..Cn-1) ∈ C implies (Cn-1,C0,C1…..Cn-2) ∈ C [2]
◦ The error correcting capability of cyclic codes may not be as
good as some other linear codes in general [2]
◦ Cyclic codes have wide applications in storage and
communication systems because they have efficient encoding
and decoding algorithms [2]
◦ Ways to encode & Decode the cyclic code -
1- Polynomials Method
2- Shift Register Method
8

9. Encoding of message by Cyclic Codes
Encoding process contains following steps: [3]
1. Step 1 -
Multiply u(x) by x^(n−k)
1. Step 2 -
Divide x^(n−k).u(x) by g(x)
1. Step 3 -
Form the code word b(x) + x^(n−k).u(x)
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Remainder = parity bit
Eg-Generator polynomial for (7,4) is given by X^3+X+1. Determine the code
vector in systematic form for sequence 1011

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Shift Register Method [3]

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16. Decoding of message by Cyclic Codes
Decoding process contains following steps:
1. Step 1 -
Syndrome computation
1. Step 2 -
Association of the syndrome to an error pattern
1. Step 3 -
Error correction
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17. Syndrome Decoding
Syndrome polynomial to be the remainder of. division by
generator polynomial: s(x) = r(x) mod g(x) = s0 + s1x + ··· + sn-
k-1xn-k-1.
Every codeword is a multiple of g(x), so codewords have
syndrome 0
Example - For a (7,4) code dimension the g(x)=X^3+X+1 and
received sequence is R = 1001000. Find the sequence is valid or
not & Correct it
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20. 20

21. Applications of Cyclic Codes
1. In DNA Codes (A-G-T-C) [5]
2. In Steganography [6]
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22. 24
LDPC Codes

23. Introduction
◦ Low-density parity-check [7]
◦ Originally invented and investigated by Gallager in 1960 [7]
◦ High SNR
◦ High Data Rate
N bit long LDPC code in terms of M no. of Parity Check
equations and describing those Parity Checks with a M * N
Parity Check Matrix H. [7]
M - No. of parity check equations
N - No. of bits in the codeword
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➢ At receiver message bit can be easily decoded by
comparing two copies bit by bit
➢ Speed of communication is high
➢ But unfortunately this process of repetition gets
fails whenever same bit is missing

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➢ Decoder fails to completely decode the message bit
➢ Biggest challenge for the communication engineers
➢ Also it doubles the message length no matter what
is the number of erasers
➢ This efficiency issue can be expressed by
CODE RATE

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1. Lower code is a more expensive to design
2. Every bit we transmit has some cost
3. So there is a balance to strike between the code rate
and the probability of failure
We need a coding strategy with just enough protection
bits to prevent failure
& For that purpose LDPC codes arrives

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(a) (b)
(c) (d)

28. 30
➢ Overlapping approach extended
➢ Process of decoding parity check bits goes very much complex
➢ Slow down the communication process

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● What we need is -
Code with very fast decode operations [7]
● We left with final problem
How can we extend this overlapping subset approach to
work quickly over very long message [7]

30. Representations of LDPC code
➢ An [n, k, d] LDPC code may be represented by a Tanner graph G(V, E)
➢ The parity-check matrix H of the LDPC code consists of
rows and
Columns
The set of vertices Vv(G) and Vp(G) are called variable and
parity-check vertices, respectively
32

31. Representations of a [16, 4, 4] LDPC code [11]
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32. Algorithms
➢ Encoder [8]
Label-and-decide Method
Pseudo Tree
Triangular Factorisation
Tanner Graph Method
➢ Decoder
Bit Flip Algorithm
Long Domain Based Sum product Algorithm
Probability Domain Based Sum product Algorithm
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33. 35
Flow-chart for LDPC matrix creation

34. 36
Start
M : rows
N: columns
onePerCol:no of 1’s
Iter : no.of iterations
Ensures rows & columns
have same number of 1’s
1’s added to rows that have
single 1 or have none of
them
End

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38. 40
Lets see the difference of LDPC Coded and uncoded Codeword[10]
https://matlab.mathworks.com/

39. Application of LDPC Codes
In storage devices In communication devices
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40. 42
Sr.
No.
Title of paper Publication & Author Summary
01 Error Correction Technique
Based On Forward Error
Correction For H.264 Codec
2012 IEEE
J.A.S.N.Jayasooriya,
Y.L.Midipolawatta,
M.B.Dissanayake
An efficient error correction algorithm is
proposed to improve the reconstructed video
quality in an error-prone network
02 On Capacity of Network
Error Correction Coding
with Random Errors
2018 IEEE letter
Wangmei Guo,
Dan He and Ning Cai
Non-linear coding at the source and linear
coding at intermediate nodes over the general
multicast network, which is proved to be able
to achieve strictly higher transmission rate than
linear NEC
03 Single-Error Detection and
Correction for Duplication
and Substitution Channels
2020 IEEE
Yuanyuan Tang, Yonatan
Yehezkeally, Student Member,
IEEE, Moshe Schwartz, Senior
Member, IEEE, and Farzad
Farnoud, Member, IEEE
They focused on two noise models, where the
substitution error is either restricted to occur in
an inserted copy during one of the duplication
events, or may occur at any position in the
string
Literature survey

41. 43
Sr.
No.
Title of paper Publication & Author Summary
04 Efficient Decoding of Short
Length Linear Cyclic Codes
IEEE COMMUNICATIONS
LETTERS, VOL. 19, NO. 4,
APRIL 2015
A number of iterative decoding algorithms
have been proposed in the literature for the
decoding of linear block codes.The technique
proposed in this paper also utilises the BP
algorithm with the key difference of
incorporating the permutation into the
message passing process
04 Construction of MDS
Convolutional Error-
correcting Network Codes
Over Cyclic Networks
IEEE Transactions on
Communications ( Volume: 65,
Issue: 6, June 2017)
In this paper, a construction algorithm was
presented for ring-based MDS linear network
codes over cyclic networks. This algorithm
was first developed for acyclic networks, and
then network de-cycling was used to extend
it to general cyclic networks. Finally, the
complexity of the proposed algorithm was
analyzed
05 Cyclic Low Density Parity
Check Codes With the
Optimum Burst Error
Correcting Capability
Received October 2, 2020,
accepted October 15, 2020,
date of publication October 21,
2020, date of current version
November 2, 2020.
The paper presents a new scheme of cyclic
codes suitable for the correction of burst
errors.y. Considering the parity check matrix
of these codes, bounds for determining their
burst error correction were presented

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Sr.
No.
Title of paper Publication & Author Summary
07 Error-Prediction LDPC and
Error-Recovery Schemes for
Highly Reliable Solid-State
Drives (SSDs)
IEEE Journal of Solid-State
Circuits
Year: 2013
The whole system in this paper was
constructed of a PC and the SSD system. If
they are implemented in ASIC, the gate
count of the EP-LDPC codec in the NAND
controller is similar to the conventional
LDPC
08 New Decoding Scheme for
LDPC Codes Based on
Simple Product Code
Structure
JOURNAL OF
COMMUNICATIONS AND
NETWORKS, VOL. 17, NO. 4,
AUGUST 2015
The proposed decoding scheme adopts a
simple product code structure to have a
strong post-processing for good error
correcting performance of LDPC codes. It
mainly takes advantage of combining two
independently received soft-decision data for
the same codeword.
05 On Efficient Concatenation
of LDPC Codes With
Constrained Codes
© 2015 IEEE. Publication
Chi Dinh Nguyen1,2,3, Kui
Cai1 , Bingrui Wang1 , and
Yan Hong1
In the paper they proposed two new methods
for concatenating the LDPC codes with the
constrained codes. The proposed designs
deployed the nibble-based technique to
generate k constrained sequences. I

43. Performance comparison
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44. Future scope
◦ Interesting area of future research is the study of how the
presence of caches would affect the correlation in the data
input to the ECC memory, and whether there is any
systematic pattern there that can be exploited by the
optimization algorithms
◦ Furthermore we can make it possible to implement
parallelizable decoders.
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45. Conclusion
To conclude this presentation I can say that error codes have
been developed to specifically protect against both random bit
errors and burst errors.
Real-time systems must consider tradeoffs between coding delay
and error protection.
To conclude second part of the presentation I Also can say that
the cyclic codes have a very good performance in detecting
single-bit errors, double errors, an odd number of errors, and
burst errors & LDPC code is a linear error correcting code, a
method of transmitting a message over a noisy transmission
channel.
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46. References
[1]J.A.S.N.Jayasooriya, Y.L.Midipolawatta, M.B.Dissanayake,”Error Correction Technique Based On
Forward Error Correction For H.264 Codec”(2012)
[2]Shuhei Tanakamaru,Yuki Yanagihara, Ken Takeuchi,”Error-Prediction LDPC and Error-Recovery
Schemes for Highly Reliable Solid-State Drives(SSDs) “(2013)
[3]Mohamed Ismail, Stojan Denic, and Justin Coon,”Efficient Decoding of Short Length Linear Cyclic
Codes”(2015)
[4]Beomkyu Shin,Seokbeom Hong,Hosung Park,Jong-SeonNo,andDong-JoonShin,”New Decoding Scheme
for LDPC Codes Based on Simple Product Code Structure”(2015)
[5]Chi Dinh Nguyen1,2,3, Kui Cai1, Bingrui Wang1, and Yan Hong1,”On Efficient Concatenation of LDPC
Codes with Constrained Codes “(2015)
[6]Vahid SAMADI-KHAFTARI1, Morteza ESMAEILI1,2, Thomas Aaron GULLIVER2, ”Construction of
MDS Convolutional Error-correcting Network Codes Over Cyclic Networks”(2017)
[7]Wangmei Guo, Dan He and Ning Cai,”On Capacity of Network Error Correction Coding with Random
Errors “(2018)
[8]Yuanyuan Tang, Yonatan Yehezkeally,”Single-Error Detection and Correction for Duplication and
Substitution Channels”(2020)
[9]SINA VAFI ,”Cyclic Low Density Parity Check Codes With the Optimum Burst Error Correcting
Capability”(2020) 48

47. References
[1] https://en.wikipedia.org/
[2]Cunsheng Ding,Cyclotomic Constructions of Cyclic Codes With Length Being the Product of Two
Primes
IEEE TRANSACTIONS ON INFORMATION THEORY,VOL.58,NO.4,APRIL 2012
[3]Riaz Ahmad Qamar, Mohd Aizaini Maarof and Subariah Ibrahim ,An efficient encoding algorithm for
(n, k) binary cyclic codes ,Indian Journal of Science and Technology
[4]Vahid SAMADI-KHAFTARI1, Morteza ESMAEILI1,2, Thomas Aaron GULLIVER2 ,Construction of
MDS Convolutional Error-correcting Network Codes Over Cyclic Networks ,2017
[5]BahattinYildiza,∗,IrfanSiapb,CycliccodesoverF2[u]/(u4−1) andapplicationstoDNAcodes ,Elsevier Article
[6]Houda JOUHARI1 and El Mamoun SOUIDI2,Application of Cyclic Codes over Z4 in Steganography
[7]Robert G. Gallager,Low Density PArity check codes , 1963
[8]Yuanyuan Tang, Yonatan Yehezkeally,”Single-Error Detection and Correction for Duplication and
Substitution Channels”(2020)
[9]SINA VAFI ,”Cyclic Low Density Parity Check Codes With the Optimum Burst Error Correcting
Capability”(2020)
[10] https://github.com/giuliomarin/tlc/blob/master/ldpc/LDPC.m
[11]Thomas J. Richardson and Rüdiger L. Urbanke,Efficient Encoding of Low-Density Parity-Check Codes 49

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THANK
YOU ..!!