Lec-9 Convolutiona Turbo TCM.pdf

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11/29/2013

Advance Coding Theory Information Theory and Coding ECE581 ECE533

Convolutional Codes 

Convolutional ConvolutionalCodes Codes

  

Introduction Encoder Tree/Trelis Encoders Structure

Nikesh Bajaj [email protected] Asst. Prof., ECE Dept. Lovely Professional University

Channel Coding 

By Nikesh Bajaj

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Classification

Classes of Channel Coding Error Correcting Codes BCH Block Codes

Block Codes

Error Correcting Codes

Convolutional Codes

Linear Block Codes

Linear Block Codes

Cyclic Code ReedSolomon

Convolutional Codes

(Hamming, Golay, MDS, Perfect)

Cyclic Codes Fire code, Burst code

BCH Reed -Solomon By Nikesh Bajaj

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Convolutional Code (n0, k0)         

Input m / information frame– k0 Output /codeword frame u1u2 -- n0 Code rate R m Constraint Length K Tree Code / Stream Code Input data bits Wordlength = Kk0 Blocklength = Kn0 Convolutional code – LTI Sliding block code 5

u1 First coded bit u1 ,u2

Output coded bits

u2

Second coded bit

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Encoding 

State Diagram

M= 10101001101010101 u1

m

u1 u2

u2

u1



Equation:

m

u1 u2

u2

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u1

m

u1 u2

u2

Tree 

Trellis

Tree

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Trellis

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Trellis

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 

Polynomial

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By Nikesh Bajaj

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G

What you should know  



Diagram of Convolutional Coders Determining n0 k0 constraint length K code rate r Draw   



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Practice

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State Diagram of any coder Trellis Diagram of any coder Writing G in polynomial form

“See example in book”

Encoding any stream with 

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

FIR/IIR x=D Size(G) =k0 x no



Given circuit State diagram and Trellis Diagram

By Nikesh Bajaj

Other Encoders

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Code(?,?)

G

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TCM: Concept of Coded Mod.

Generating Poly



Trellis Coded Modulation    

 By Nikesh Bajaj

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Modulation QPSK, 8-PSK Euclidean distance and Hamming distance Constellation of QPSK and 8-PSK

Reference: Ranjan Bose, Do go through book By Nikesh Bajaj

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Modulation… Euclidean Distance

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Constellation diagram

By Nikesh Bajaj

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Constraint sequence of symbols

Example  

By Nikesh Bajaj

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   

Turbo Code: Encoder

1993, ICC, Berou et all BER=10-5 at Eb/N0 =0.7dB with ½ encoder Good for Low SNR, not for high –RS Block or convolutional code Uses Interleaver   

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Turbo Codes 

Consider TCM Encoding

PCCC SCCC HCCC By Nikesh Bajaj

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Example

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