Observable convolutional codes defined over Zpr with the Predictable Degree Property admit minimal input/state/output representations that preserve structural properties under scalar restriction. We make use of this fact to present Rosenthal's decoding algorithm for these convolutional codes. When combined with the Greferath-Vellbinger algorithm and a modified version of the Torrecillas-Lobillo-Navarro algorithm, the decoding problem of convolutional codes over Zpr reduces to selecting two decoding algorithms for linear block codes over a field. Finally, we analyze both the theoretical and practical error-correction capabilities of the combined algorithm as well as its time complexity.

翻译：在Zpr上定义且具有可预测次数特性的可观测卷积码，其最小输入/状态/输出表示在标量限制下能够保持结构特性。我们利用这一事实，为这类卷积码提出了Rosenthal解码算法。当该算法与Greferath-Vellbinger算法以及Torrecillas-Lobillo-Navarro算法的改进版本相结合时，Zpr上卷积码的解码问题可简化为选择两种适用于域上线性分组码的解码算法。最后，我们分析了该组合算法的理论与实际纠错能力及其时间复杂度。