VTU E&C,TCE CBCS[NEW] 5th Sem Information Theory and Coding Module-4 notes(15 and 17 scheme).
INFORMATION THEORY AND CODING B.E., V Semester, Electronics & Communication Engineering / Telecommunication Engineering [As per Choice Based Credit System (CBCS) scheme] Subject Code:15EC54 and 17EC54 Module-4 Error Control Coding: Introduction, Examples of Error control coding, methods of Controlling Errors, Types of Errors, types of Codes, Linear Block Codes: matrix description of Linear Block Codes, Error Detection and Error Correction Capabilities of Linear Block Codes, Single Error Correcting hamming Codes, Table lookup Decoding using Standard Array. Binary Cyclic Codes: Algebraic Structure of Cyclic Codes, Encoding using an (n-k) Bit Shift register, Syndrome Calculation, Error Detection and Correction (Sections 9.1, 9.2, 9.3, 9.3.1, 9.3.2, 9.3.3 of Text 1). Question paper pattern: The question paper will have ten questions Each full question consists of 16marks. There will be 2 full questions (with a maximum of four sub questions) from each module. Each full question will have sub questions covering all the topics under a Module. The students will have to answer 5 full questions, selecting one full question From each module. Text Book: 1. Information Theory and Coding, Muralidhar Kulkarni , K.S. Shivaprakasha, Wiley India Pvt. Ltd, 2015, ISBN:978-81-265-5305-1 2. Digital and analog communication systems, K. Sam Shanmugam, John Wiley India Pvt. Ltd, 1996. 3. Digital communication, Simon Haykin, John Wiley India Pvt. Ltd, 2008. Reference Books: 1. ITC and Cryptography, Ranjan Bose, TMH, II edition, 2007 2. Principles of digital communication, J. Das, S. K. Mullick, P. K. Chatterjee, Wiley, 1986 - Technology & Engineering 3. Digital Communications – Fundamentals and Applications, Bernard Sklar, Second Edition, Pearson Education, 2016, ISBN: 9780134724058. 4. Information Theory and Coding, K.N.Hari bhat, D.Ganesh Rao, Cengage Learning, 2017.
![FORMULAS FOR REFERENCE
MODULE – 4 (error control coding and binary cyclic codes)
Chapter -1 error control coding
The code vector is given by
[C]= [D] [G]
The Message vector is given by
𝟐 𝒌
The Parity check matrix is given by
[H]= [ 𝑷 𝑻
: 𝑰 𝒏−𝒌 ] or [ 𝑰 𝒏−𝒌 : 𝑷 𝑻
]
The generator matrix is given by
[G]= [𝑰 𝑲: P] or [𝑷 ∶ 𝑰 𝑲]
The syndrome is given by
S=R𝑯 𝑻
or r𝑯 𝑻
The corrected code vector is given by
C=R+E
The single error correcting (n, k) Hamming code has the following parameters
Code length: n 𝟐 𝒏−𝒌−𝟏
Number of message bits : k n-𝒍𝒐𝒈 𝟐 (n+1)
Number of parity check bits: (n-k)
Error correcting capability: t =
𝒅 𝒎𝒊𝒏 − 𝟏
𝟐
Error correcting capability: 𝒅 𝒎𝒊𝒏 − 𝟏
𝑯 𝑻
is given by
𝑯 𝑻
= [
𝑷
𝑰 𝒏−𝒌
] or [
𝒅 𝒌 𝑿 (𝒏−𝒌)
𝑰 𝒏−𝒌
]
HAMMING BOUND (perfect code or not)
𝟐 𝒏−𝒌
𝐂𝐢
𝐧𝒕
𝒊=𝟎](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
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VTU E&C,TCE CBCS[NEW] 5th Sem Information Theory and Coding Module-4 notes(15 and 17 scheme).
- 1. INFORMATION THEORY AND CODING 5th SEM E&C JAYANTHDWIJESH H P M.tech (DECS) Assistant Professor – Dept of E&C B.G.S INSTITUTE OF TECHNOLOGY (B.G.S.I.T) B.G Nagara, Nagamangala Tq, Mandya District- 571448
- 2. FORMULAS FOR REFERENCE MODULE – 4 (error control coding and binary cyclic codes) Chapter -1 error control coding The code vector is given by [C]= [D] [G] The Message vector is given by 𝟐 𝒌 The Parity check matrix is given by [H]= [ 𝑷 𝑻 : 𝑰 𝒏−𝒌 ] or [ 𝑰 𝒏−𝒌 : 𝑷 𝑻 ] The generator matrix is given by [G]= [𝑰 𝑲: P] or [𝑷 ∶ 𝑰 𝑲] The syndrome is given by S=R𝑯 𝑻 or r𝑯 𝑻 The corrected code vector is given by C=R+E The single error correcting (n, k) Hamming code has the following parameters Code length: n 𝟐 𝒏−𝒌−𝟏 Number of message bits : k n-𝒍𝒐𝒈 𝟐 (n+1) Number of parity check bits: (n-k) Error correcting capability: t = 𝒅 𝒎𝒊𝒏 − 𝟏 𝟐 Error correcting capability: 𝒅 𝒎𝒊𝒏 − 𝟏 𝑯 𝑻 is given by 𝑯 𝑻 = [ 𝑷 𝑰 𝒏−𝒌 ] or [ 𝒅 𝒌 𝑿 (𝒏−𝒌) 𝑰 𝒏−𝒌 ] HAMMING BOUND (perfect code or not) 𝟐 𝒏−𝒌 𝐂𝐢 𝐧𝒕 𝒊=𝟎
- 3. Chapter-2 binary cyclic codes The Non systematic cyclic code vector is given by V(X) =D(X) g(X) The systematic cyclic : The remainder polynomial R(X) is given by R(X) = 𝑫 𝑿 𝑿 𝒏−𝒌 𝒈(𝑿) The code vector is given by [V] = [R][D] The parity check polynomial is given by h (x) =𝒙 𝒏 +1 / g(x) The code vector is given by [V] = [R][D]