In this paper we investigate the relation between the QAM input
information rate (IR) of multi-carrier (MC) systems and single carrier
(SC) systems transmitting through inter-symbol interference (ISI)
additive white Gaussian noise (AWGN) channels. In particular,
considering uniform power spectrum transmission, we conjecture that
given the channel, the IR corresponding to an SC input distribution is
greater than IR corresponding to an MC input distribution. We give an
intuitive justification of our conjecture and confirm it by means of
numerical analysis on two sets of randomly generated channels.