U. Glaeser

Therefore, an improvement in error-probability performance of this channel can be accomplished by
limiting the length of strings of alternating symbols in code sequences to four. For the NRZI type of
recording, this can be achieved by a code that limits the runs of successive ones to three. Note that the set
of minimum distance error events is smaller than in the case with no ITI. Thus, performance improvement
can be accomplished by higher rate codes that would not provide any gain on the ideal channel.
Channel equalization to the EPR4 target introduces cross-correlation among noise samples for a range
of current linear recording densities (see [27] and references therein). The following result was obtained
in [27]:
Proposition 3. Error events �(D) such that
take the following form:
Again, the set of minimum distance error events is smaller than in the ideal case (white noise), and
performance improvement can be provided by codes which would not give any gain on the ideal channel.
For example, since all minimum distance error events have odd parity, a single parity check code can be
used.
Future Directions
Soft-Output Decoding of Modulation Codes
Detection and decoding in magnetic recording systems is organized as a concatenation of a channel
detector, an inner decoder, and an outer decoder, and as such should benefit from techniques known as
erasure and list decoding. To declare erasures or generate lists, the inner decoder (or channel detector)
needs to assess symbol/sequence reliabilities. Although the information required for this is the same one
necessary for producing a single estimate, some additional complexity is usually required. So far, the
predicted gains for erasure and list decoding of magnetic recording channels with additive white Gaussian
noise were not sufficient to justify increasing the complexity of the channel detector and inner and outer
decoder; however, this is not the case for systems employing new magneto-resistive reading heads, for
which an important noise source, thermal asperities, is to be handled by passing erasure flags from the
inner to the outer decoder.
In recent years, one more reason for developing simple soft-output channel detectors has surfaced.
The success of turbo-like coding schemes on memoryless channels has sparked the interest in using them
as modulation codes for ISI channels. Several recent results show that the improvements in performance
turbo codes offer when applied to magnetic recording channels at moderate linear densities are even
more dramatic than in the memoryless case [12,29]. The decoders for turbo and low-density parity check
codes (LDPC) either require or perform much better with soft input information which has to be supplied
by the channel detector as its soft output. The decoders provide soft outputs which can then be utilized by
the outer Reed–Solomon (RS) decoder [22]. A general soft-output sequence detection was introduced
in [11], and it is possible to get information on symbol reliabilities by extending those techniques [21,31].
Reversed Concatenation
Typically, the modulation encoder is the inner encoder, i.e., it is placed downstream of an error-correction
encoder (ECC) such as an RS encoder; this configuration is known as standard concatenation (Fig. 34.45).
This is natural since otherwise the ECC encoder might well destroy the modulation properties before
© 2002 by CRC Press LLC
l−1
∑
2
∆ 2 ( �)
= ∆min �( D)
( – 1)
i
D i
= , l ≥ 3, l odd
i=0