  In this paper, we show that the soft-decision input to the main decoder in an
SST Viterbi decoder is regarded as the innovation as well from the viewpoint of
mutual information and mean-square error. It is assumed that a code sequence is
transmitted symbol by symbol over an AWGN channel using BPSK modulation. Then
we can consider the signal model, where the signal is composed of the
signal-to-noise ratio (SNR) and the equiprobable binary input. By assuming that
the soft-decision input to the main decoder is the innovation, we show that the
minimum mean-square error (MMSE) in estimating the binary input is expressed in
terms of the distribution of the encoded block for the main decoder. It is
shown that the obtained MMSE satisfies indirectly the known relation between
the mutual information and the MMSE in Gaussian channels. Thus the derived MMSE
is justified, which in turn implies that the soft-decision input to the main
decoder can be regarded as the innovation. Moreover, we see that the
input-output mutual information is connected with the distribution of the
encoded block for the main decoder.
