Corrections to “An Innovations Approach to Viterbi Decoding of Convolutional Codes” [May 19 2704-2722

Abstract

In the above article <xref ref-type="bibr" rid="ref1" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">[1]</xref> , we correct errors in Section III-B. The corrections are related to the joint distribution of the inputs to the main decoder which corresponds to a branch in the code trellis for the main decoder. Note that as far as the distribution of the input corresponding to a single code symbol is concerned, the results in Section III-B are correct. We have noticed that <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha$ </tex-math></inline-formula> in Proposition 12 ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\beta$ </tex-math></inline-formula> in Proposition 14) has another meaning, which has made it possible to derive the joint distribution of the inputs corresponding to the whole branch. Corrections are based on this important observation.