In contrast to the prevalent assumption of rich multipath 
in information theoretic analysis of wireless channels, 
physical channels exhibit sparse multipath, especially 
at large bandwidths. We propose a model for sparse 
multipath fading channels and present results on the 
impact of sparsity on non-coherent capacity and reliability 
in the wideband regime. From a capacity perspective, sparse 
channels are asymptotically coherent: the gap between 
coherent and non-coherent extremes vanishes in the limit of 
large signal space dimensions without the need for peaky 
signaling. From a reliability viewpoint, there is a 
fundamental tradeoff between channel diversity and 
learnability that can be optimized to maximize the error 
exponent at any rate by appropriately choosing the 
signaling duration as a function of bandwidth.