1. Synchronization of Turbo Codes Based on Online Statistics
Jian Sun and Matthew C. Valenti
Wireless Communication Research Laboratory
Lane Dept. of Comp. Sci. and Elec. Engr.
West Virginia University
May
Greetings, every one. Today I am going to present my recent research on timing synchronization of turbo coded systems.

2. Outline Necessity of timing synchronization Concepts
Effective signal-to-noise ratio (SNR)
Online statistic
Algorithm to compensate coding gain loss
Over-sampling and interpolation
Joint estimation of SNR and timing offset
Simulation results and conclusions
Future work
This is the outline of this presentation. First, I am going to talk about the importance of timing synchronization, which is the motivation of our work. A few concepts are introduced, including the effective signal-to-noise ratio and online statistics. Then we propose an algorithm to compensate coding gain loss. Simulation results justify our approach. And modifications might be applied to our method for future work.

3. Necessity of Timing Synchronization in Turbo Coded Systems
Turbo codes are attractive because of its near-Shannon-limit BER performance in very low SNR environments.
Traditional synchronization methods will fail because of low SNR.
Improper synchronization will render the turbo coded system great loss of coding gain.
Prior work done by Mielczarek and Svensson [1]
Viewing turbo decoders as SNR improvers
Post decoding combination
Two turbo decoders in parallel
First is the necessity of timing synchronization in turbo coded systems. Turbo codes are well-known for their near-Shannon-limit performance in very low SNR environments. Although this is very attractive, there are some issues. First, at very low SNR situation, traditional symbol-by-symbol synchronization will fail. Second, turbo codes are sensitive to improper timing. Even small deviations could cause large degradation in the coding gain. Very interesting work has been published by Mielczarek and Svensson. They looked upon the turbo decoders as SNR improver, and
[1] B. Mielczarek and A. Svensson, “Timing error recovery in turbo coded systems on AWGN channels," IEEE Trans. Comm., vol. 50, pp , October 2002.

4. BER Performance of Turbo Coded System with Fixed Timing Offset
Timing offset is the difference of the actual sampling time and the symbol’s ending point.
Simulations show the effect of fixed timing offset on BER performance.
Simulation settings
Following cdma2000 encoder structure
Coding rate = 1/3
Interleaver size = 1530
Constraint length = 4
10 iterations
Raised-cosine pulse shaping with roll-off factor 0.5 10 -1 10
τ = 0.2T -2 10
τ = 0.1T -3 10
Bit Error Rate -4 10
1 dB -5 10
τ = 0 -6
0.25 dB 10 -7 10
0.2
0.4
0.6
0.8 1
1.2
1.4
1.6
1.8
Eb/N0 (dB)

5. Effective SNR Received signal Effective SNR Mean squared error of ISI
Energy per symbol
Intersymbol interference
Additive noise
Transmitted data
Pulse shaping function

6. Effective SNR and Timing Offset3
Simulation settings:
Uncoded BPSK signal in AWGN channel
Raised-cosine pulse shaping with roll-off factor 0.5
The effective SNR is a function of both channel SNR and timing offset.
The shape and position of the curves changes with the channel SNR. 2
SNR = 2 dB 1
Effective SNR (dB) -1
SNR = 1 dB -2
SNR = 0 dB -3 -4 -5
-0.5
-0.4
-0.3
-0.2
-0.1
0.1
0.2
0.3
0.4
0.5
Timing Offset (T)

7. Joint Estimation of SNR and Timing Offset
Effective SNR is a function of both timing offset and SNR on channel.
With multiple values of effective SNR, we can solve the equation for timing offset and SNR simultaneously.
Assuming semi-static channel, we need to estimate the effective SNR on basis of each frame without knowledge of transmitted data.
To generate multiple effective SNR estimates, multiple samples of each symbol in a frame are taken.

8. Over-Sampling and Interpolation
Decoder infrastructure { r }
Online s 1
, n 1
Channel
Received
Estimation
Signal r ( t )
Joint
Matched
Estimation
Filter { r } s
Algorithm
Online 2
, n 2
Channel
Estimation
SNR
Timing
Estimation
Estimation
Interpolated
Decoded
Samples
Data
Inter-
Turbo
polator
Decoder

9. Interpolation Method Linear interpolation
Information loss due to improper timing cannot be recovered
Generate satisfactory results with sufficient large number of samples per symbol
More subtle interpolation methods
Boost up noise which is dominant in the environment where turbo codes are implemented
Do not improve SNR r2 r0 r1 t1 t2
Linear interpolation

10. Online Statistics Summers and Wilson’s approach [2]
The calculation does not require knowledge of the data.
The statistic itself is a random variable.
The statistic is a one-to-one map to SNR.
The statistics can be used to calculate the effective SNR associated with sample sequences
The joint estimation algorithm can be implemented with statistics directly.
[2] T. A. Summers and S. G. Wilson, “SNR mismatch and online estimation in turbo decoding,” IEEE Trans. Comm., vol. 46, pp , April 1998.

11. Joint Estimation Algorithm
Curve fitting algorithm
Minimum mean-squared error approach
Needs to store all possible curve shapes
Vulnerable to fluctuation of statistic values
Linear approximation
Solution forβ0 andτ

12. Simulation Settings Turbo encoder Interleaver size = 1530
Constraint length = 4
Code rate = 1/3
Encoder structure follows cdma2000 specifications
Semi-static AWGN channel
BPSK modulation
Raised-cosine roll-off pulse shaping with roll-off factor 0.5
Timing offset is a random variable with uniform distribution between -0.5T and 0.5T, but it is fixed in each frame
Timing offset differs from frame to frame
Turbo decoder
10 iterations are conducted before hard-decision is made
Linear approximation is used for joint estimation algorithm
Linear interpolation is used to regenerate signals

13. BER Performance of Turbo Coded System with 2 Samples/Symbol
About 0.2 dB loss due to linear interpolation
About 0.7 dB loss due to error in estimation of timing offset
About 0.8 dB loss due to error in joint estimation of channel SNR and timing offset. 10
Estimated Timing and SNR -1 10
Known SNR, Estimated Timing
Known Timing and SNR
Perfect Timing -2 10 -3 10
Bit Error Rate 10 -4 -5 10 -6 10 -7 10 -8 10
0.2
0.4
0.6
0.8 1
1.2
1.4
1.6
1.8
Eb/N0 (dB)

14. BER Performance of Turbo Coded System with 4 Samples/Symbol10
Almost no loss due to linear interpolation.
Less than 0.2 dB coding gain loss from error in joint estimation of channel SNR and timing offset.
Implementation with one turbo decoder and low additional complexity and latency.
Estimated Timing and SNR -1
Known Timing and SNR 10
Perfect Timing -2 10
Bit Error Rate -3 10 10 -4 -5 10 -6 10 10 -7
0.2
0.4
0.6
0.8 1
1.2
1.4
Eb/N0 (dB)

15. Possible Improvements
Simulation results indicate that BER performance can be improved without changing the decoder structure by
Using better estimators that make estimation with smaller variance;
Using better interpolators that recover more information by combining samples without loss of SNR.
Refine estimation using turbo principles.
The iterative nature of turbo decoder enables us to rebuild reliable decision using intermediate decoding results.
The intermediate decoding result can be directed back to form a loop.
The joint estimation of channel SNR and timing offset can be refined with decision-feedback.

16. Conclusions
Effective SNR can be used to evaluate loss in coding gains for turbo coded systems caused by improper timing.
With slight additional complexity, the proposed system can recover coding gains to 0.2 dB within the performance of perfect timing situation with 4 samples per symbol.