Corrections to "An Innovations Approach to Viterbi Decoding of Convolutional Codes"

TL;DR

This paper provides corrections to a previous work on Viterbi decoding of convolutional codes, clarifying the joint distribution of decoder inputs and rectifying earlier errors for improved accuracy.

Contribution

It identifies and corrects errors in the joint distribution analysis of decoder inputs, offering a refined understanding of the decoding process.

Findings

Corrected the joint distribution of decoder inputs in the trellis

Clarified the meaning of alpha and beta in the propositions

Enhanced the accuracy of the original decoding analysis

Abstract

We correct errors in Section III-B of the above-titled paper. 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 alpha in Proposition 12 (beta 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.