  Blind deconvolution is an ubiquitous non-linear inverse problem in
applications like wireless communications and image processing. This problem is
generally ill-posed since signal identifiability is a key concern, and there
have been efforts to use sparse models for regularizing blind deconvolution to
promote signal identifiability. Part I of this two-part paper establishes a
measure theoretically tight characterization of the ambiguity space for blind
deconvolution and unidentifiability of this inverse problem under unconstrained
inputs. Part II of this paper analyzes the identifiability of the
canonical-sparse blind deconvolution problem and establishes surprisingly
strong negative results on the sparsity-ambiguity trade-off scaling laws.
Specifically, the ill-posedness of canonical-sparse blind deconvolution is
quantified by exemplifying the dimension of the unidentifiable signal sets. An
important conclusion of the paper is that canonical sparsity occurring
naturally in applications is insufficient and that coding is necessary for
signal identifiability in blind deconvolution. The methods developed herein are
applied to a second-hop channel estimation problem to show that a family of
subspace coded signals (including repetition coding and geometrically decaying
signals) are unidentifiable under blind deconvolution.
