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III. Turbo Codes

III. Turbo Codes. Worldwide Applications & Standards Data Storage Systems DSL Modem / Optical Communications 3G (Third Generation) Mobile Communications Digital Video Broadcast (DVB) Satellite Communications IEEE 802.16 WiMAX …. Applications of Turbo Codes. Basic Concept of Turbo Codes.

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III. Turbo Codes

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  1. III. Turbo Codes

  2. Worldwide Applications & Standards Data Storage Systems DSL Modem / Optical Communications 3G (Third Generation) Mobile Communications Digital Video Broadcast (DVB) Satellite Communications IEEE 802.16 WiMAX … Applications of Turbo Codes

  3. Basic Concept of Turbo Codes Invented in 1993 by Alian Glavieux, Claude Berrou and Punya Thitimajshima Basic Structure: a) Recursive Systematic Convolutional (RSC) Codes b) Parallel concatenation and Interleaving c) Iterative decoding

  4. Recursive Systematic Convolutional Codes Non Systematic Convolutional Code Recursive Systematic Convolutional Code c1 c1 + + + + + c2 c2 g1=[1 1 1] g2=[1 0 1] g1=[1 1 1] g2=[1 0 1] G=[1g2/g1] G=[g1 g2]

  5. 00 00 00 11 11 11 11 11 11 00 00 00 10 10 10 01 01 01 01 01 01 10 10 10 Non-Recursive Encoder Trellis Diagram 00 00 00 s0 (0 0) 11 11 11 11 s1 (1 0) 00 10 10 s2 (0 1) 01 01 01 s3 (1 1) 10

  6. 00 00 00 11 11 11 11 11 11 00 00 00 10 10 10 01 01 01 01 01 01 10 10 10 Systematic Recursive Encoder Trellis Diagram 00 00 00 s0 (0 0) 11 11 11 11 s1 (1 0) 00 10 10 s2 (0 1) 01 01 01 s3 (1 1) 10

  7. Non-Recursive & Recursive Encoders • Non Recursive and recursive encoders both have the same trellis diagram structure • Generally Recursive encoders provide better weight distribution for the code • The difference between them is in the mapping of information bits to codewords

  8. Parallel Concatenation with Interleaving • Two component RSC Encoders in parallel separated by an Interleaver • The job of the interleaver is to de-correlate the encoding process of the two encoders • Usually the two component encoder are identical xk : Systematic information bit yk(1) : Parity bit from the first RSC encoder yk(2) : Parity bit from the second RSC encoder xk xk RSC Encoder 1 yk(1) π RSC Encoder 2 yk(2) 1/3 Turbo Encoder

  9. Interleaving Permutation of data to de-correlate encoding process of both encoders If encoder 1 generates a low weight codeword then hopefully the interleaved input information would generate a higher weight codeword By avoiding low weight codewords the BER performance of the turbo codes could improve significantly

  10. Examples: Block Interleaver Fu-hua Huang

  11. Examples: Pseudo Random Interleaver Fu-hua Huang

  12. Examples: Circular-Shift Interleaver p(i) = (a*i+s) mod L a=3, s=0, L=8 Fu-hua Huang

  13. Turbo Decoder Iteratively exchanging information between decoder 1 and decoder 2 before making a final deciding on the transmitted bits rk xk* RSC Decoder 1 π-1 π RSC Decoder 2

  14. Turbo Codes Performance Principles of Turbo Codes: Keattisak Sripiman  http:www.kmitl.ac.th/dslabs/TurboCodes

  15. Serial Concatenation with Interleaving • Two component RSC Encoders in sereies separated by an Interleaver • The job of the interleaver two de-correlate the encoding process of the two encoders RSC Encoder 1 RSC Encoder 2 π r2=n2/k2 r1=n1/k1 rtot=k1k2/n1n2

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