  In order to describe the exotic nuclear structure in unstable odd-$A$ or
odd-odd nuclei, the deformed relativistic Hartree Bogoliubov theory in
continuum has been extended to incorporate the blocking effect due to the odd
nucleon. For a microscopic and self-consistent description of pairing
correlations, continuum, deformation, blocking effects, and the extended
spatial density distribution in exotic nuclei, the deformed relativistic
Hartree Bogoliubov equations are solved in a Woods-Saxon basis in which the
radial wave functions have a proper asymptotic behavior at large $r$. The
formalism and numerical details are provided. The code is checked by comparing
the results with those of spherical relativistic continuum Hartree Bogoliubov
theory in the nucleus $^{19}$O. The prolate deformed nucleus $^{15}$C is
studied by examining the neutron levels and density distributions.
