U. Glaeser

FIGURE 34.56 Block diagram of a RAM-based DFE.
problem and it can, in fact, be altogether avoided through a technique that is called Tomlinson/Harashima
precoding.
Performance differences between zero-forcing and minimum mean-square equalizers tend to be considerably
smaller in the DFE case than for the LE, and as a result it becomes more dificult to reap SNR
benefits from the modulation code. It can be proved that DFE is the optimum receiver with no detection
delay. If delay is allowed, it is better to use trellis-based detection algorithms.
RAM-Based DFE Detection
Decision feedback equalization or RAM-based DFE is the most frequent alternative to PRML detection.
Increase of bit density leads to significant nonlinear ISI in the magnetic recording channel. Both the
linear DFE [12,26] and PRML detectors do not compensate for the nonlinear ISI. Furthermore, the
implementation complexity of a Viterbi detector matched to the PR channel grows exponentially with
the degree of channel polynomial. Actually, in order to meet requirements for a high data transfer rate,
high-speed ADC is also needed. In the RAM-based DFE [19,24], the linear feedback section of the linear
DFE is replaced with a look-up table. In this way, detector decisions make up a RAM address pointing
to the memory location that contains an estimate of the post cursor ISI for the particular symbol sequence.
This estimate is subtracted from the output of the forward filter forming the equalizer output. Look-up
table size is manageable and typically is less than 256 locations. The major disadvantage of this approach
is that it requires complicated architecture and control to recursively update ISI estimates based on
equalizer error.
Detection in a Trellis
A trellis-based system can be simply described as a FSM (Finite State Machine) whose structure may be
displayed with the aid of a graph, tree, or trellis diagram. A FSM maps input sequences (vectors) into
output sequences (vectors), not necessarily of the same length. Although the system is generally nonlinear
and time-varying, linear fixed trellis based systems are usually met. For them,
where a is a constant, i [0,∞) is any input sequence and F(i [0,∞)) is the corresponding output sequence. It
is assumed that input and output symbols belong to a subset of a field. Also, for any d > 0, if x [0,∞) =
F(i [0,∞)) and i′ l = il−d, i ′ [0,d) = 0 [0,d) then F(i ′ [0,∞) ) = x [0,∞) ′ , where xl′ = xl−d, x [0,d) ′
, = 0 [0,d). It is easily
verified that F(⋅) can be represented by the convolution, so that x = i ∗ h, where h is the system impulse
© 2002 by CRC Press LLC
Sampled channel data
Forward
Filter
+ _
_
+
RAM
containing
estimates of ISI
Equalizer errror
RAM
address
F( a⋅ i [0,∞) ) = a⋅F( i [0,∞) )
F( i ′
[0,∞) + i ″
[0,∞) ) = F( i ′
[0,∞) ) + F( i ″
[0,∞) )
Recovered data
D
D
.....
D