Weijun Tan, Haitao Xia and J' R' Cruz

1
Erasure Detection Algorithms for Magnetic
Recording Channels

• Weijun Tan, Haitao Xia and J. R. Cruz
• Communications Signal Processing Laboratory
• The University of Oklahoma

2
Outline

• Media Defect Model
• Precoding Performance Loss
• BCJR Analysis of Erasure Detection
• Improved Algorithm
• Simulation Results
• Summary

3
Media Defect Model
Envelope
1-?
? 0.5
Partial erasure
Full erasure
? 1.0
t
4
Precoding Loss

• LDPC coded ME2PR4 channel
• AWGN
• Ideally detected erasures
• Several precoders
• Asymptotic density evolution (DE) analysis of
  code (3,30)
• Simulation of code (4376,3,30)

5
Numerical Results

• Precoding causes a loss of 0.20.7 dB
• 1/(1D) is the best precoder

• DE and simulation results are consistent
• The ranking of the precoders does not change with
  erasures

6
BCJR Analysis

• BCJR algorithm
• Erasure section
• No useful signal, zini

7
Erasure Detection
Non-Precoded 1/(1D)-Precoded

• ?i(s',s,yi0)gt?i(s',s,yi?0)
• ai(s?)gtai(s??)
• ßi(s?)gt ßi(s??)
• (s'?s,yi0) selected
• Non-precoded 0000, 1111, 1010, RLL(0,GI)
• 1/(1D) precoded 0000, 1111, RLL(0,k)

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BCJR LLRs
Nonprecoded, ?0.5
1/(1D)-Precoded, ?0.5
1/(1D)-Precoded, ?1.0
Non-Precoded, ?1.0
1/(1D)-Precoded, ?0.5
Non-Precoded, ?0.5

• Amplitude of BCJR LLRs attenuated
• Long runs of zi 0
• Erasures

• Can be used to detect (partial) erasures in
  combination with RLL codes

9
Improved Algorithm

• Tentative BCJR decisions

• Broader RLL checks
• Runs of
• Runs of
• Runs of

10
Simulation Results

• ME2PR4/(1D),Sc2.995
• LDPC (4608,3751),R0.814
• L192, k 28
• The new algorithm is slightly better

• EPR4/(1D2),Sc2.995
• LDPC (4608,4096),R0.899
• L128, k 28
• The new algorithm is 0.5 dB better

11
Summary

• 1/(1D) is the best precoder for the ME2PR4
  channel, if needed
• BCJR analysis of erasure detection
• RLL(0,k) for 1/(1D)-precoded ME2PR4
• RLL(0,GI) for non-precoded ME2PR4
• BCJR LLR amplitude thresholding
• Improved algorithm
• Better performance