Multipath interference is an ubiquitous phenomenon in modern communication
systems. The conventional way to compensate for this effect is to equalize the
channel by estimating its impulse response by transmitting a set of training
symbols. The primary drawback to this type of approach is that it can be
unreliable if the channel is changing rapidly. In this paper, we show that
randomly encoding the signal can protect it against channel uncertainty when
the channel is sparse. Before transmission, the signal is mapped into a
slightly longer codeword using a random matrix. From the received signal, we
are able to simultaneously estimate the channel and recover the transmitted
signal. We discuss two schemes for the recovery. Both of them exploit the
sparsity of the underlying channel. We show that if the channel impulse
response is sufficiently sparse, the transmitted signal can be recovered
reliably.