  Sparse intersymbol-interference (ISI) channels are encountered in a variety
of high-data-rate communication systems. Such channels have a large channel
memory length, but only a small number of significant channel coefficients. In
this paper, trellis-based equalization of sparse ISI channels is revisited. Due
to the large channel memory length, the complexity of maximum-likelihood
detection, e.g., by means of the Viterbi algorithm (VA), is normally
prohibitive. In the first part of the paper, a unified framework based on
factor graphs is presented for complexity reduction without loss of optimality.
In this new context, two known reduced-complexity algorithms for sparse ISI
channels are recapitulated: The multi-trellis VA (M-VA) and the
parallel-trellis VA (P-VA). It is shown that the M-VA, although claimed, does
not lead to a reduced computational complexity. The P-VA, on the other hand,
leads to a significant complexity reduction, but can only be applied for a
certain class of sparse channels. In the second part of the paper, a unified
approach is investigated to tackle general sparse channels: It is shown that
the use of a linear filter at the receiver renders the application of standard
reduced-state trellis-based equalizer algorithms feasible, without significant
loss of optimality. Numerical results verify the efficiency of the proposed
receiver structure.
