  This paper considers the input-erasure Gaussian channel. In contrast to the
output-erasure channel where erasures are applied to the output of a linear
time-invariant (LTI) system, here erasures, known to the receiver, are applied
to the inputs of the LTI system. Focusing on the case where the input symbols
are independent and identically distributed (i.i.d)., it is shown that the two
channels (input- and output-erasure) are equivalent. Furthermore, assuming that
the LTI system consists of a two-tap finite impulse response (FIR) filter, and
using simple properties of tri-diagonal matrices, an achievable rate expression
is presented in the form of an infinite sum. The results are then used to study
the benefits of joint multicell processing (MCP) over single-cell processing
(SCP) in a simple linear cellular uplink, where each mobile terminal is
received by only the two nearby base-stations (BSs). Specifically, the analysis
accounts for ergodic shadowing that simultaneously blocks the mobile terminal
(MT) signal from being received by the two BS. It is shown that the resulting
ergodic per-cell capacity with optimal MCP is equivalent to that of the two-tap
input-erasure channel. Finally, the same cellular uplink is addressed by
accounting for dynamic user activity, which is modelled by assuming that each
MT is randomly selected to be active or to remain silent throughout the whole
transmission block. For this alternative model, a similar equivalence results
to the input-erasure channel are reported.
