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# Iterative Timing Recovery

Date post:11-Jan-2016
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Iterative Timing Recovery. Aleksandar Kavčić Division of Engineering and Applied Sciences Harvard University based on a tutorial by Barry, Kavčić, McLaughlin, Nayak & Zeng And on research by Motwani and Kavčić. Outline. Motivation Timing model Conventional timing recovery - PowerPoint PPT Presentation
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Soft-output Detector for Channels with Deletion/InsertionDIMACS-04
Harvard University
And on research by
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Outline
Motivation
Soft decision algorithm
Division of Engineering and Applied Sciences
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Motivation
In most communications (decoding) scenarios, we assume perfect timing recovery
This assumption breaks down, particularly at low signal-to-noise ratios (SNRs)
But, turbo-like codes work exactly at these SNRs
Need to take timing uncertainty into account
Division of Engineering and Applied Sciences
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t
Channel
Xn
YL
S
R
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0
-T
T
2T
3T
t
1
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Discrete samples form a Markov chain.
t
t
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decoding
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Set up math model for timing error (Markov).
Build separate stationary trellis to characterize the channel and source.
Form a full trellis.
Derive an algorithm to perform the Maximum a posteriori probability (MAP) estimation of the timing offset and the input bits
Division of Engineering and Applied Sciences
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0
-T
T
2T
3T
t
1
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State Transition Diagram:
State Transition Probability:
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1 deletion states: 0
1 2-sample state: 2
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0
T
2T
3T
4T
5T
6T
7T
8T
9T
10T
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Total number of states at each time interval:
Trellis length = n (block length). (note that each branch may have different number of outputs).
Full states set:
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-2T
0
-T
T
2T
3T
1
0
h(t)
3T/5
-2T/5
8T/5
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2
3
4
5
6
10-4
10-3
10-2
10-1
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timing error
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Conclusion
Conventional timing recovery fails at low SNR because it ignores the error-correction code.
Iterative timing recovery exploits the power of the code.
Performance close to perfect timing recovery
Only marginal increase in complexity compared to system that uses conventional turbo equalization/decoding
Division of Engineering and Applied Sciences
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2
3
4
5
6
10-4
10-3
10-2
10-1
SNR per bit (dB)
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Capacity
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Xk { 0, 1 }
Sequence y is a subsequence of sequence x
Symbol xk is deleted with probability
Division of Engineering and Applied Sciences
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Ulmann 1968, upper bounds on the capacities of deletion channels
Diggavi&Grossglauser 2002, analytic lower bounds on capacities of deletion channels
Mitzenmacher 2004, tighter analytic lower bounds
Division of Engineering and Applied Sciences
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Let K(m) denote the number of received symbols
per m transmitted symbols
Asymptotically, we have A received symbols per transmitted symbol
For the deletion channel,
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If X is a first-order Markov source (transition matrix P),
then Y is also a first-order Markov source (transition matrix Q)
Division of Engineering and Applied Sciences
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to upper-bound H(Y|X)
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Codes?

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