U. Glaeser

FIGURE 34.45 Standard concatenation.
FIGURE 34.46 Reversed concatenation.
passing across the channel; however, this scheme has the disadvantage that the modulation decoder,
which must come before the ECC decoder, may propagate channel errors before they can be corrected.
This is particularly problematic for modulation encoders of very high rate, based on very long block size.
For this reason, a good deal of attention has recently focused on a reversed concatenation scheme, where
the encoders are concatenated in the reversed order (Fig. 34.46). Special arrangements must be made to
ensure that the output of the ECC encoder satisfies the modulation constraints. Typically, this is done
by insisting that this encoder be systematic and then re-encoding the parity information using a second
modulation encoder (the “parity modulation encoder”), whose corresponding decoder is designed to
limit error propagation; the encoded parity is then appended to the modulation-encoded data stream
(typically a few merging bits may need to be inserted in between the two streams in order to ensure that
the entire stream satisfies the constraint). In this scheme, after passing through the channel the modulationencoded
data stream is split from the modulation-encoded parity stream, and the latter is then decoded
via the parity modulation decoder before being passed on to the ECC decoder. In this way, many channel
errors can be corrected before the data modulation decoder, thereby mitigating the problem of error
propagation. Moreover, if the data modulation encoder has high rate, then the overall scheme will also
have high rate because the parity stream is relatively small.
Reversed concatenation was introduced in [3] and later in [23]. Recent interest in the subject has been
spurred on by the introduction of a lossless compression scheme, which improves the efficiency of
reversed concatenation [15], and an analysis demonstrating the benefits in terms of reduced levels of
interleaving [8]; see also [9]. Research on fitting soft decision detection into reversed concatenation can
be found in [7,33].
References
1. R. Adler, D. Coppersmith, and M. Hassner, “Algorithms for sliding-block codes,” IEEE Trans. Inform.
Theory, vol. 29, no. 1, pp. 5–22, Jan. 1983.
2. J. Ashley and B. Marcus, “Time-varying encoders for constrained systems: an approach to limiting
error propagation,” IEEE Trans. Inform. Theory, 46 (2000), 1038–1043.
3. W. G. Bliss, “Circuitry for performing error correction calculations on baseband encoded data to
eliminate error propagation,” IBM Tech. Discl. Bull., 23 (1981), 4633–4634.
4. W. G. Bliss, “An 8/9 rate time-varying trellis code for high density magnetic recording,” IEEE Trans.
Magn., vol. 33, no. 5, pp. 2746–2748, Sept. 1997.
5. T. Conway, “A new target response with parity coding for high density magnetic recording,” IEEE
Trans. Magn., vol. 34, pp. 2382–2386, 1998.
6. T. Cover, “Enumerative source encoding,” IEEE Trans. Inform. Theory, pp. 73–77, Jan. 1973.
© 2002 by CRC Press LLC