  We propose two approximate algorithms for MAP decoding on tail-biting
trellises. The algorithms work on a subset of nodes of the tail-biting trellis,
judiciously selected. We report the results of simulations on an AWGN channel
using the approximate algorithms on tail-biting trellises for the $(24,12)$
Extended Golay Code and a rate 1/2 convolutional code with memory 6.
