Noise-Predictive Turbo Equalization for Partial Response Channels

1
Noise-Predictive Turbo Equalization for Partial
Response Channels Sharon Aviran, Paul H. Siegel
and Jack K. Wolf Department of Electrical and
Computer Engineering, UCSD E-mail saviran,
psiegel, jwolf_at_ucsd.edu
Abstract
LDPC Decoding
Iterative Decoding for Magnetic Recording Channels
Today's digital magnetic recording
devices employ a partial-response maximum
likelihood (PRML) detection scheme in the
readback process. A PRML system uses an equalizer
to shape the channel response to a partial
response (PR) polynomial. The noisy samples from
the PR channel are then decoded by a Viterbi
detector. We assume that the noise at the
readback is AWGN. Hence, the noise sequence at
the output of the equalizer is colored. As bit
densities grow, the PR equalizer leads to
substantial noise enhancement, which increasingly
affects the performance of PRML systems. To
overcome performance degradation, the class of
NPML detectors was introduced. An NPML detector
incorporates a noise prediction (NP) process into
the branch metric computation of the Viterbi
detector. Recently, iterative decoding
and detection methods were introduced and applied
to PR channels. These techniques have been shown
to offer significant improvements in detection
performance. Specifically, we are interested in a
system that includes a soft-output channel
detector that is matched to the PR channel and an
iterative decoder for the error-correction code.
The two components operate independently while
communicating soft information to each other.
This scheme is often referred to as turbo
equalization. However, noise enhancement and
coloring still occur at the output of the
equalizer, leading to performance degradation.
We design an iterative decoding system for PR
channels that takes the noise coloration into
account. We incorporate a noise prediction module
into a standard turbo equalization scheme,
consisting of a BCJR detector and an LDPC
decoder. Noise prediction is imbedded into the
branch metric computation of the BCJR algorithm.
It is performed selectively, based on soft
information that is obtained from the turbo
equalizer. We demonstrate the performance
improvement that is achieved by the proposed
scheme.

• We are interested in iterative decoders for LDPC
  codes due to their remarkable performance
• LDPC codes are linear block codes, defined by a
  sparse parity check matrix
• A graphical description of the code consists of
  bit nodes and parity check nodes. An edge
  connects a bit node to a parity check node if
  that bit is involved in that parity equation
• Decoding is done by passing messages along the
  lines of the graph

• Iterative decoders use soft information as inputs
  and produce soft information as outputs (SISO)
• ECC scheme should incorporate a PR channel
  detector to cope with ISI
• Iterative decoding schemes use a SISO channel
  detector, e.g., a MAP (BCJR) decoder
• A MAP decoder computes the a posteriori bit
  probability (APP) assuming an AWGN and given the
• Channel model (trellis)
• Noisy observations and noise variance
• Prior soft information on the bits
• Schemes of the following type were applied to
• PR channels
• Soft information is iterated between the channel
• decoder and the ECC decoder
• This is called Turbo Equalization

Noise-Predictive Turbo Equalization
Partial-Response Equalization

• Procedure is similar to the memoryless channel
  case. There are 3 differences
• Obtaining Soft information Turbo Equalization
  block replaces LDPC decoder
• Making noise decisions additional past bit
  decisions are required to determine a noise term
• Iterating with the channel updated noisy
  observations and corresponding variances are fed
  into
• the BCJR decoder. They are incorporated in
  the computation of updated branch metrics

• Todays digital magnetic recording devices employ
  a partial-response maximum likelihood (PRML)
  detection scheme in the readback process
• A PRML system uses an equalizer to shape the
  channel response to a particular polynomial
  target, called a partial response (PR) polynomial
• Equalizer is followed by a Viterbi detector (VD),
  matched to the target shape

1. Making Reliable Noise Decisions

Outline of a single iteration

• Perform a single BCJR pass followed by T LDPC
  iterations
• Determine all reliable bits and make reliable bit
  decisions
• Make noise decisions from available bit decisions
• Estimate noise terms by linearly combining
  neighboring noise decisions
• Subtract noise estimates from channels noisy
  observations
• Feed new values and variances to BCJR for next
  iteration
• Priors to BCJR remain the extrinsic information
  of the LDPC

1. Linear Noise Prediction

Performance for PR4 and EPR4
Summary
Noise Prediction and PRML Detection

• Partial-response equalization leads to noise
  enhancement and coloration
• We proposed a new iterative decoding scheme for
  PR channels that takes the noise coloration into
  account
• Scheme uses a selective noise prediction process
  that is imbedded into the channel detector
• Future work includes
• Application to perpendicular recording channels
• Incorporation of soft decisions
• Feedback of bit decisions into LDPC and BCJR
  decoders

• Assume a zero-forcing PR equalizer
• Its output can be written as
• Equalizer determines colored noise model and
  autocorrelation

1. Iterating with the Channel

• Subtract new noise estimates from noisy
  observations
• Updated noisy observations have lower noise power
• Recompute likelihoods, given updated observations
  and updated variances. Input as new priors to LDPC

• Modify VDs branch metric computation for each
  state transition sj -gt sk
• Estimate past noise samples by subtracting past
  bit decisions from past outputs
• Take past bit decisions from the survivor path
  associated with state sj
• Assign past noise estimates in a predictor to
  estimate current noise term
• Subtract current noise estimate from current
  equalizer output
• Calculate branch metric with new value

Acknowledgement. We would like to thank Joseph
Soriaga and Panu Chaichanavong for their
assistance in the implementation of this scheme.