Turbo coding basics and simulation over Rayleigh fading channel

1
Turbo coding basics and simulation over Rayleigh
fading channel

• Yu Song, Muzhou Jiang
• Apr. 26, 2007

2
Outline

• Introduction to Turbo Codes
• Turbo Encoder
• Turbo Decoder
• Rayleigh Fading Channel intro
• Simulations

3
Introduction

• High-performance error correction codes
• Devised by Berrou et al. 1 in 1993
• Advantages
• Low BER at SNR close to Shannon limit
• Or for a certain BER, power can be decreased
• Drawbacks
• High decoder complexity
• Relatively high latency due to interleaving and
• iterations when decoding

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Turbo Encoder

• Two recursive systematic convolutional encoder in
  parallel with an interleaver preceding one of
  them

Payload bits
Input
RSC1
Optional Puncturing
Parity bits 1
Interleaver
Parity bits 2
RSC2
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Turbo Encoder for UMTS
Xk
Zk
D
D
D
Xk
Interleaver
Zk
D
D
D
Xk
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Turbo Decoder

• Log-Likelihood Ratio (LLR) is used as input to
  decoder
• Matched filter must be scaled (ak is channel
  response, is variance of nk )

(Received signal)
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Turbo Decoder Architecture

• Soft-In-Soft-Out, Modified Viterbi Algorithm
• Iterative Decoding

Extrinsic Information 1
RSC DEC. 1
LLR(Xk)
Extrinsic Information 2
LLR(Zk)
RSC DEC. 2
Interleaver
De- Inter
LLR(Zk)
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Rayleigh fading

• Good approx. for time-variant channel in
  densely-built places (Manhattan)
• Signals transmitted through multiple reflective
  paths, no line-of-sight path
• pdf

9
Rayleigh fading modeling

• Channel model
• is a Rayleigh random variable,
• are both Gaussian R.V.

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Simulation set-up

• BPSK Modulation
• Turbo Code
• Generators g1 g2 1 0 1 1, 1 1 0 1
• Frame size of 640 bits
• Linear-log-MAP algorithm is used in decoder
• Convolutional Code
• K 4, Rate ½
• g1 1 0 1 1, g2 1 1 0 1

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Simulation results -- AWGN
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Simulation results -- Rayleigh
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Simulation results -- Iterations
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References

• 1 C. Berrou, A. Glavieux and P. Thitimajshima,
  Near Shannon Limit Error-Correcting Coding and
  Decoding Turbo Codes, Proc. 1993 IEEE
  International Conference on Communications, pp
  1064-1070, 1993
• 2 http //www.wikipedia.com
• 3 M. C. Valenti and J. Sun, The UMTS Turbo Code
  and an Efficient Decoder Implementation Suitable
  for Software-Defined Radios, International
  Journal of Wireless Information Networks, Vol. 8,
  No. 4, pp. 203-215, 2001
• 4 M. C. Valenti and J. Sun, Turbo codes,
  Chapter 12 in Handbook of RF and Wireless
  Technologies, Edited by F. Dowla Editor, Newnes
  Press, 2004, pp. 375-399
• 5 B. Sklar, Rayleigh Fading Channels in Mobile
  Digital Communication Systems Part I
  Characterization, IEEE Communications Magazine,
  pp. 90-100, July 1997
• 6 http//www.iterativesolutions.com/Matlab.htm
• 7 L. F. Choy, I. J. Fair, W. A. Krzymien,
  Complexity-Performance Trade-offs in Turbo Codes
  for IMAT-2000, 2000 IEEE Vehicular Technology
  Conference, pp. 2568-2575