Dynamic information storage or retrieval – Binary pulse train information signal – Binary signal gain processing
Reexamination Certificate
1998-07-31
2001-02-06
Hindi, Nabil (Department: 2753)
Dynamic information storage or retrieval
Binary pulse train information signal
Binary signal gain processing
C360S053000
Reexamination Certificate
active
06185173
ABSTRACT:
FIELD OF INVENTION
The present invention relates to the recording and reproduction of binary data in storage systems for digital computers (such as magnetic and optical disk drives), particularly to a sampled amplitude read channel employing a trellis sequence detector matched to a code constraint for detecting a binary sequence during a read operation, and a post processor for correcting errors in the detected binary sequence using samples of the read signal and an error syndrome generated from redundancy bits encoded into the recorded data.
BACKGROUND OF THE INVENTION
In computer storage devices, such as optical and magnetic disk drives, sampled amplitude read channels employing partial response (PR) signaling with maximum likelihood (ML) sequence detection have provided a substantial increase in storage capacity by allowing for significantly higher linear bit densities. Partial response signaling refers to a particular method for transmitting symbols represented as analog pulses through a communication medium. The benefit is that at the signaling instances (baud rate) there is no intersymbol interference (ISI) from other pulses except for a controlled amount from immediately adjacent, overlapping pulses. Allowing the pulses to overlap in a controlled manner leads to an increase in the symbol rate (linear recording density) without sacrificing performance in terms of signal-to-noise ratio (SNR).
Partial response channels are characterized by the polynomials
(1−D) (1+D)
n
where D represents a delay of one symbol period and n is an integer. For n=1,2,3, the partial response channels are referred to as PR4, EPR4 and EEPR4, with their respective frequency responses shown in FIG.
1
A. The channel's dipulse response, the response to an isolated symbol, characterizes the transfer function of the system (the output for a given input). With a binary “1” bit modulating a positive dipulse response and a binary “0” bit modulating a negative dipulse response, the output of the channel is a linear combination of time shifted dipulse responses. The dipulse response for a PR4 channel (1−D
2
) is shown as a solid line in FIG.
1
B. Notice that at the symbol instances (baud rate), the dipulse response is zero except at times t=0 and t=2. Thus, the linear combination of time shifted PR4 dipulse responses will result in zero ISI at the symbol instances except where immediately adjacent pulses overlap.
It should be apparent that the linear combination of time shifted PR4 dipulse responses will result in a channel output of +2, 0, or −2 at the symbol instances depending on the binary input sequence. The output of the channel can therefore be characterized as a state machine driven by the binary input sequence, and conversely, the input sequence can be estimated or demodulated by running the signal samples at the output of the channel through an “inverse” state machine. Because noise will obfuscate the signal samples, the inverse state machine is actually implemented as a trellis sequence detector which computes a most likely input sequence associated with the signal samples.
Operation of a PR4 trellis sequence detector is understood from its state transition diagram shown in FIG.
2
A. Each state
100
is represented by the last two input symbols (in NRZ after precoding), and each branch from one state to another is labeled with the current input symbol in NRZ
102
and the corresponding sample value
104
it will produce during readback. The demodulation process of the PR4 sequence detector is understood by representing the state transition diagram of
FIG. 2A
as a trellis diagram shown in FIG.
2
B. The trellis diagram represents a time sequence of sample values and the possible recorded input sequences that could have produced the sample sequence. For each possible input sequence, an error metric is computed relative to a difference between the sequence of expected sample values that would have been generated in a noiseless system and the actual sample values output by the channel. For instance, a Euclidean metric is computed as the accumulated square difference between the expected and actual sample values. The input sequence that generates the smallest Euclidean metric is the most likely sequence to have created the actual sample values; this sequence is therefore selected as the output of the sequence detector.
To facilitate the demodulation process, the sequence detector comprises path memories for storing each of the possible input sequences and a corresponding metric. A well known property of the sequence detector is that the paths storing the possible input sequences will “merge” into a most likely input sequence after a certain number of sample values are processed, as long as the input sequence is appropriately constrained. In fact, the maximum number of path memories needed equals the number of states in the trellis diagram; the most likely input sequence will always be represented by one of these paths, and these paths will eventually merge into one path (i.e., the most likely input sequence) after a certain number of sample values are processed.
The “merging” of path memories is understood from the trellis diagram of
FIG. 2B
where the “survivor” sequences are represented as solid lines. Notice that each state in the trellis diagram can be reached from one of two states; that is, there are two transition branches leading to each state. With each new sample value, the Viterbi algorithm recursively computes a new error metric and retains a single survivor sequence for each state corresponding to the minimum error metric. In other words, the Viterbi algorithm will select one of the two input branches into each state since only one of the branches will correspond to the minimum error metric, and the paths through the trellis corresponding to the branches not selected will merge into the paths that were selected. Eventually, all of the survivor sequences will merge into one path through the trellis which represents the most likely estimated data sequence to have generated the sample values as shown in FIG.
2
B.
In some cases, if the input sequence is not appropriately constrained through the use of a channel code, the path memories will not merge into one survivor sequence. Consider the PR4 trellis shown in
FIG. 2B
; an input sequence of all zeros or all ones will prevent the paths from merging which leads to multiple possible survivor sequences output by the detector. Data sequences which prevent the path memories from merging are referred to as “quasi-catastrophic” data sequences since they result in quasi-catastrophic errors in the output sequence. In order to avoid quasi-catastrophic errors, a channel code is typically employed which codes out of the recorded data all sequences which can prevent the path memories from merging.
Even if the quasi-catastrophic data sequences are coded out of the input sequence, the sequence detector can still make an error in detecting the output sequence if enough destructive noise is present in the read signal. The possible output sequences are different from one another by a minimum Euclidean distance; a detection error typically occurs when the signal noise breaches this minimum distance between valid output sequences.
FIGS. 3A-3D
illustrate the sample error sequences associated with the dominant minimum distance error events of a PR4 sequence detector in NRZ, PR4, EPR4 and EEPR4 space, respectfully. In general, a higher order sequence detector will outperform a lower order sequence detector due to the number of data samples the error event affects. Consider, for example, the first error event in the NRZ space shown in FIG.
3
A. This error event generates two noise samples which corrupt two data samples (two output bits) in the PR4 space of
FIG. 3B
, four noise samples in the EPR4 space of
FIG. 3C
, and four noise samples with two having increased magnitude in the EEPR4 space of FIG.
3
D. This “spreading out” of the error event reduces the probability of a detection error.
A minimum
Bliss William G.
Livingston Jay N.
Cirrus Logic Inc.
Hindi Nabil
Sheerin Howard H.
Shifrin Dan A.
Violette J. P.
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