论文标题
关于广义串联代码和矩阵产物代码的解码
On Decoding of Generalized Concatenated Codes and Matrix-Product Codes
论文作者
论文摘要
Zinoviev在1970年代引入了广义的串联代码。文献中有多种类型的代码以其他名称知道，可以看作是广义的串联代码。示例包括矩阵 - 产品代码，多级代码和广义级联代码。 1970年代和1980年代开发了广义级联代码的解码算法。但是，它们的使用似乎并没有像其他名称所知道但可以看作是广义级联代码所知的代码一样广泛。 在本文中，我们回顾了串联代码，广义串联代码和矩阵产物代码的解码算法，并阐明了矩阵 - 产品代码与广义串联代码之间的连接。我们对串联代码的解码算法提出了一个较小的改进。我们还将解码算法从仅错误解码器扩展到了错误和射击解码器。此外，在矩阵产物代码的情况下，我们在解码算法的计算复杂性上提高了上限，其中内部代码的发电机矩阵是非列列的。
Generalized concatenated codes were introduced in the 1970s by Zinoviev. There are many types of codes in the literature that are known by other names that can be viewed as generalized concatenated codes. Examples include matrix-product codes, multilevel codes and generalized cascade codes. Decoding algorithms for generalized concatenated codes were developed during the 1970s and 1980s. However, their use does not appear to be as widespread as it should, especially for codes that are known by other names but can be viewed as generalized concatenated codes. In this paper we review the decoding algorithms for concatenated codes, generalized concatenated codes and matrix-product codes, and clarify the connection between matrix-product codes and generalized concatenated codes. We present a small improvement to the decoding algorithm for concatenated codes. We also extend the decoding algorithms from errors-only decoders to error-and-erasure decoders. Furthermore, we improve the upper bound on the computational complexity of the decoding algorithm in the case of matrix-product codes where the generator matrix for the inner code is non-singular by columns.
