  A complete representation of the Martin boundary of killed random walks on a
half-space $\Z^{d-1}\times\N^*$ is obtained. In particular, it is proved that
the corresponding Martin boundary is homemorphic to the half-sphere ${\cal
S}^d_+ = \{z\in\R^{d-1}\times\R_+ : |z|=1\}$. The method is based on a
combination of ratio limits theorems and large deviation techniques.
