  From the pioneering work of Winter [Phys. Rev. 124, 452 (1961)], a magnetic
domain wall of Bloch type is known to host a special wall-bound spin-wave mode,
which corresponds to spin-waves being channeled along the magnetic texture.
Using micromagnetic simulations, we investigate spin-waves travelling inside
Bloch walls formed in thin magnetic media with perpendicular-to-plane magnetic
anisotropy and we show that their propagation is actually strongly
nonreciprocal, as a result of dynamic dipolar interactions. We investigate
spin-wave non-reciprocity effects in single Bloch walls, which allows us to
clearly pinpoint their origin, as well as in arrays of parallel walls in stripe
domain configurations. For such arrays, a complex domain-wall-bound spin-wave
band structure develops, some aspects of which can be understood qualitatively
from the single-wall picture by considering that a wall array consists of a
sequence of up/down and down/up walls with opposite non-reciprocities.
Circumstances are identified in which the non-reciprocity is so extreme that
spin-wave propagation inside individual walls becomes unidirectional.
