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

The Two-Tap Input-Erasure Gaussian Channel and its Application to Cellular Communications