1 research outputs found
Characterization of Graph-cover Pseudocodewords of Codes over
Linear-programming pseudocodewords play a pivotal role in our understanding
of the linear-programming decoding algorithms. These pseudocodewords are known
to be equivalent to the graph-cover pseudocodewords. The latter
pseudocodewords, when viewed as points in the multidimensional Euclidean space,
lie inside a fundamental cone. This fundamental cone depends on the choice of a
parity-check matrix of a code, rather than on the choice of the code itself.
The cone does not depend on the channel, over which the code is employed. The
knowledge of the boundaries of the fundamental cone could help in studying
various properties of the pseudocodewords, such as their minimum pseudoweight,
pseudoredundancy of the codes, etc. For the binary codes, the full
characterization of the fundamental cone was derived by Koetter et al. However,
if the underlying alphabet is large, such characterization becom is more
involved. In this work, a characterization of the fundamental cone for codes
over is discussed.Comment: 5 pages, to be presented in ITW 2010, Dublin, Irelan