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The Bases Associated with Trellises of a Lattice

It is well known that the trellises of lattices can be employed to decode efficiently. It was proved in [1] and [2] that if a lattice L has a finite trellis under the coordinate system {Wi}i=1n, then there must exist a basis (b1,b2, ···, bn) of L such that Wi = span(bi) for 1 ≤ i ≤ n. In this letter, we prove this important result in a completely different method, and give an efficient method to compute all bases of this type.