It is well known that there is a correspondence between convolutional codes and discrete-time linear systems over finite fields. In this paper, we employ the linear systems representation of a convolutional code to develop a decoding algorithm for convolutional codes over the erasure channel. In this kind of channel, which is important due to its use for data transmission over the Internet, the receiver knows if a received symbol is correct. We study the decoding problem using the state space description of a convolutional code, and this provides in a natural way additional information. With respect to previously known decoding algorithms, our new algorithm has the advantage that it is able to reduce the decoding delay as well as the computational effort in the erasure recovery process. We describe which properties a convolutional code should have in order to obtain a good decoding performance and illustrate it with an example.

众所周知，卷积码与有限域上的离散时间线性系统之间存在对应关系。在本文中，我们采用卷积码的线性系统表示来开发用于擦除信道上的卷积码的解码算法。在这种由于用于通过互联网传输数据而很重要的信道中，接收器知道接收到的符号是否正确。我们使用卷积码的状态空间描述来研究解码问题，这以一种自然的方式提供了附加信息。相对于先前已知的解码算法，我们的新算法的优点是能够减少解码延迟以及擦除恢复过程中的计算工作量。