Simultaneous Code/Error-Trellis Reduction for Convolutional Codes Using Shifted Code/Error-Subsequences

TL;DR

This paper presents a method to simultaneously reduce the complexity of code and error-trellises in convolutional codes by using shifted subsequences, leading to more efficient decoding structures.

Contribution

It introduces a novel approach to achieve simultaneous reduction of code and error-trellises through transformations based on shifted subsequences.

Findings

Simultaneous reduction of code and error-trellises is possible under certain shift conditions.

Transformations on generator and parity-check matrices enable concurrent trellis reduction.

The method improves decoding efficiency by simplifying the trellis structures.

Abstract

In this paper, we show that the code-trellis and the error-trellis for a convolutional code can be reduced simultaneously, if reduction is possible. Assume that the error-trellis can be reduced using shifted error-subsequences. In this case, if the identical shifts occur in the subsequences of each code path, then the code-trellis can also be reduced. First, we obtain pairs of transformations which generate the identical shifts both in the subsequences of the code-path and in those of the error-path. Next, by applying these transformations to the generator matrix and the parity-check matrix, we show that reduction of these matrices is accomplished simultaneously, if it is possible. Moreover, it is shown that the two associated trellises are also reduced simultaneously.