  We introduce a new method for decoding short and moderate length linear block
codes with dense parity-check matrix representations of cyclic form, termed
multiple-bases belief-propagation (MBBP). The proposed iterative scheme makes
use of the fact that a code has many structurally diverse parity-check
matrices, capable of detecting different error patterns. We show that this
inherent code property leads to decoding algorithms with significantly better
performance when compared to standard BP decoding. Furthermore, we describe how
to choose sets of parity-check matrices of cyclic form amenable for
multiple-bases decoding, based on analytical studies performed for the binary
erasure channel. For several cyclic and extended cyclic codes, the MBBP
decoding performance can be shown to closely follow that of maximum-likelihood
decoders.
