  In this paper, we derive the exact input/output transfer functions of the
optimal a-posteriori probability channel detector for a general ISI channel
with erasures. Considering three channel impulse responses of different memory
as an example, we compute the BP and MAP thresholds for regular spatially
coupled LDPC codes with joint iterative detection and decoding. When we compare
the results with the thresholds of ISI channels with Gaussian noise we observe
an apparent inconsistency, i.e., a channel which performs better with erasures
performs worse with AWGN. We show that this anomaly can be resolved by looking
at the thresholds from an entropy perspective. We finally show that with
spatial coupling we can achieve the symmetric information rates of different
ISI channels using the same code.
