Weijun Tan and J. R. Cruz Communications Signal Processing Laboratory The University of Oklahoma

1. Weijun Tan and J. R. Cruz Communications Signal Processing Laboratory The University of Oklahoma SNR Mismatch Effects in LDPC Coded Magnetic Recording Channels

2. Outline • SNR mismatch effects • Wrong SNR may improve performance • Sources • BCJR channel detection • LDPC decoding • Practical impact • Optimum SNR mismatch for a given system Globecom 2003

3. System Diagram Electronic noise LDPC Enc h(t)- h(t-T) EPR4 Equal BCJR LDPCDec SNR Mismatch dh(t)/dt Jitter noise Possible erasures MRC Globecom 2003

4. SNR Mismatch Effects • Simulation observations • Ideal PR channel with AWGN • No SNR mismatch effect • Equalized PR MRC • -3 dB SNR mismatch for electronic noise • -9 dB SNR mismatch for 90% jitter noise • Questions • Why is this happening? • How can we use it? Globecom 2003

5. SNR Mismatch for BCJR • BER at BCJR output not affected by SNR mismatch • Max-log-MAP • Log-MAP, if running only once • SNR mismatch scales the BCJR LLRs • Proved theoretically and verified using simulations • SNR mismatch mainly affects the LDPC decoder Globecom 2003

6. Uncoded MRC Simulation AWGN 10% AWGN+90% Jitter Globecom 2003

7. SNR Mismatch for LDPC Decoding • Channel LLR densities • Gaussian channels: known • PR channels: obtained from simulations • Use density evolution to • Compute the SNR threshold • Estimate the BER for LDPC coded MRCs • Search for an optimum SNR mismatch value Globecom 2003

8. Density Evolution • LDPC codes on binary-input memoryless symmetric-output channels • Concentration: particular vs. ensemble code when n→∞ • Convergence to cycle-free case when n→∞ • Noise threshold: when σ< σ*, • LDPC codes on PR channels • iid assumption • BER estimate Globecom 2003

9. AWGN Channel • LLR density ~ N • Two conditions that may affect the SNR mismatch effects • LLR density may not be Gaussian • The variance-to-mean ratio (VMR) ≠ 2 • What happens under these conditions? Globecom 2003

10. Gaussian Channel • LLR ~ N • m=2,ΔSNR=0 • m<2,ΔSNR<0 • m>2,ΔSNR>0 • The VMR affects SNR mismatch SNR Thresholds for LDPC (4,36) Globecom 2003

11. EPR4 Channel • Channel LLR density is approximately Gaussian • White noise • m≈2, ΔSNR=0 • Correlated noise • m≈2.3,ΔSNR<0 • In agreement with previous results SNR Thresholds for LDPC (4,36) Globecom 2003

12. EPR4 Channel with Erasures EPR4 Channel with AWGN and 3% Undetected Erasures, LDPC (4,36) Channel LLR Density Side pedestal VMR of CHANNEL DENSITY FOR EPR4 WITH 3% UNDETECTED ERASURES Globecom 2003

13. Optimum SNR Mismatch • LDPC coded MRCs • Noise: Electronic / jitter noise • Lorentzian channel Sc=3.0, equalized to EPR4 • LDPC (4,36) • BCJR 1 iteration, MP max 50 iterations • Asymptotic analysis using density evolution • Validation using simulation • A particular code of length 4376 Globecom 2003

14. BER Estimate from DE AWGN 10% AWGN+90% Jitter -3~-2 dB -10 dB Globecom 2003

15. BER Simulation AWGN 10% AWGN+90% Jitter -3~-2 dB -10 dB Globecom 2003

16. Conclusions • Causes for SNR mismatch • LLR density Gaussianity • LLR variance-to-mean ratio • If the LLR is Gaussian-like and VMR >/< 2, -/+ SNR mismatch should be used • For MRCs, VMR>2 • -3~-2 dB SNR mismatch for AWGN noise • -10 dB SNR mismatch for 90% jitter noise Globecom 2003