  Fix K a p-adic field and denote by G_K its absolute Galois group. Let K_infty
be the extension of K obtained by adding (p^n)-th roots of a fixed uniformizer,
and G_\infty its absolute Galois group. In this article, we define a class of
p-adic torsion representations of G_\infty, named quasi-semi-stable. We prove
that these representations are "explicitly" described by a certain category of
linear algebra objects. The results of this note should be consider as a first
step in the understanding of the structure of quotients of two lattices in a
crystalline (resp. semi-stable) Galois representation.
