  We introduce the notion of innovations for Viterbi decoding of convolutional
codes. First we define a kind of innovation corresponding to the received data,
i.e., the input to a Viterbi decoder. Then the structure of a
Scarce-State-Transition (SST) Viterbi decoder is derived in a natural manner.
It is shown that the newly defined innovation is just the input to the main
decoder in an SST Viterbi decoder and generates the same syndrome as the
original received data does. A similar result holds for Quick-Look-In (QLI)
codes as well. In this case, however, the precise innovation is not defined. We
see that this innovation-like quantity is related to the linear smoothed
estimate of the information. The essence of innovations approach to a linear
filtering problem is first to whiten the observed data, and then to treat the
resulting simpler white-noise observations problem. In our case, this
corresponds to the reduction of decoding complexity in the main decoder in an
SST Viterbi decoder. We show the distributions related to the main decoder
(i.e., the input distribution and the state distribution in the code trellis
for the main decoder) are much biased under moderately noisy conditions. We see
that these biased distributions actually lead to the complexity reduction in
the main decoder. Furthermore, it is shown that the proposed innovations
approach can be extended to maximum-likelihood (ML) decoding of block codes as
well.
