  We present extensions to Raghavan and Baum's reliability-output Viterbi
algorithm (ROVA) to accommodate tail-biting convolutional codes. These
tail-biting reliability-output algorithms compute the exact word-error
probability of the decoded codeword after first calculating the posterior
probability of the decoded tail-biting codeword's starting state. One approach
employs a state-estimation algorithm that selects the maximum a posteriori
state based on the posterior distribution of the starting states. Another
approach is an approximation to the exact tail-biting ROVA that estimates the
word-error probability. A comparison of the computational complexity of each
approach is discussed in detail. The presented reliability-output algorithms
apply to both feedforward and feedback tail-biting convolutional encoders.
These tail-biting reliability-output algorithms are suitable for use in
reliability-based retransmission schemes with short blocklengths, in which
terminated convolutional codes would introduce rate loss.
