Algebraic Construction of KV Trellises for Linear Block Codes

摘要

In this paper, we present an algebraic construction of Koetter-Vardy (KV) trellises. The proposed method is based on the state space expression, i.e., the state space is the image of the set of information sequences under the associated state matrix. Then combining with the homomorphism theorem, an algebraic trellis construction is obtained. We show that a tail-biting trellis constructed using the proposed method is isomorphic to the associated KV trellis (i.e., the product trellis). On the other hand, a matrix consisting of linearly independent rows of the characteristic matrix is regarded as a generalization of minimal-span generator matrices. Then we show that a KV trellis is constructed based on an extended minimal-span generator matrix. It is shown that this construction is a natural extension of the method proposed by McEliece (1996).