  The open problem of calculating the limiting spectrum (or its Shannon
transform) of increasingly large random Hermitian finite-band matrices is
described. In general, these matrices include a finite number of non-zero
diagonals around their main diagonal regardless of their size. Two different
communication setups which may be modeled using such matrices are presented: a
simple cellular uplink channel, and a time varying inter-symbol interference
channel. Selected recent information-theoretic works dealing directly with such
channels are reviewed. Finally, several characteristics of the still unknown
limiting spectrum of such matrices are listed, and some reflections are touched
upon.
