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Analysis of the efficiency of Viterbi Algorithm

Analysis of the efficiency of Viterbi Algorithm. 2003-Spring Concrete Mathematics Term Project of TEAM 2. Contents. Team Member Introduction Main Idea Interleaver Block Interleaver Scrambling Interleaver Analysis Implementation Reference. Team Member. Hyunchong Kim

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Analysis of the efficiency of Viterbi Algorithm

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  1. Analysis of the efficiency of Viterbi Algorithm 2003-Spring Concrete Mathematics Term Project of TEAM 2

  2. Contents • Team Member • Introduction • Main Idea • Interleaver • Block Interleaver • Scrambling Interleaver • Analysis • Implementation • Reference

  3. Team Member • Hyunchong Kim • Computer Graphics • Hwayoun Lee • Software Engineering • Divyan • Cryptology and Information Security

  4. Introduction ▪ Viterbi Algorithm This is where theViterbi Algorithmoperates Error Decoding Message Encoding Message

  5. Main Idea(1/2) • Viterbi Algorithm can correct distributed error but cannot correct burst error. • We try to change burst error into distributed error with Interleaver. • We implemented Viterbi Algorithm and proposed new Interleaver. • Finally, we analyzed Viterbi Algorithm with and without Interleaver.

  6. Main Idea(2/2) ▪ Improved Viterbi Algorithm Error Decoding Message Encoding Message Added Added Interleaver Deinterleaver

  7. Interleaver • Viterbi Algorithm cannot correct burst error. We add interleaver to distribute burst error. Block interleaver is currently used. We propose new interleaver, Scrambling Interleaver. • Implementation of Viterbi Algorithm http://vega.icu.ac.kr/~hena080

  8. Block Interleaver Original Message Writing 00110101110000111011 Interleaver Reading 00101011001001111011 Burst Error 00110101001001111011 The order of original Message is changed by Block Interleaver.

  9. Block Deinterleaver Reading Received Message 00110101001001111011 Burst Error Writing DeInterleaver 01110001110010110011 Distributed Error

  10. Drawback of Block Interleaver Reading Received Message 00101011001001111011 Writing DeInterleaver 00110101110000111011 Burst Error It can cause Burst Error by Block Interleaver.

  11. Scrambling Interleaver(1/3) • Scrambling • Interleaved bits -> scrambling [ Scrambling Rule ] Neighboring bits will not be adjacent and there are interval between the neighboring bits after interleaving. { 1,2,3,4, … ,n-1,n } : Choose n/2, {n/2, 1, n, n/2-1, n/2+1, …}

  12. Scrambling Interleaver(2/3) Original message Interleaved message Deinterleaved message

  13. Scrambling Interleaver(3/3) [ Original Message ] [ Interleaved Message ] [ Error ] Burst Error [ Deinterleaved Message ] Distributed Error

  14. Analysis BER 5 6 7 8

  15. Implementation • Computer Programming Language : Java • Other Tool : Matlab

  16. Reference • An analysis of the Viterbi Decoder Error Statistics for ATM and TCP/IP over Satellite Communication, Jeffrey R. Heissler & Yosry A. Barsoum • 터보부호의 인터리버 분석(http://csplab.kaist.ac.kr/~khwa/turbo.htm) • Optimal Interleaver (http://scholar.lib.vt.edu/theses/available/etd-71897-15815/unrestricted/chap3.pdf)

  17. Thank you

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