论文标题
列表对整数残留环上卷积代码的解码
List decoding of Convolutional Codes over integer residue rings
论文作者
论文摘要
$ \ zz [d] $上的卷积代码$ \ c $是$ \ zzn [d] $的$ \ zz [d] $ - $ \ zz [d] $代表$ \ zz $中的系数。在本文中，我们研究了通过擦除通道执行传输的列表解码问题的列表，也就是说，当删除其某些系数时，我们可以从CodeWord $ w \ in \ c $中恢复多少信息。我们使用$ w $的$ p $ - adic扩展以及代码的奇偶校验多项式矩阵的特定表示。从这些矩阵多项式表示中，我们递归选择了$ w $必须满足的某些方程式，并且在现场中只有系数$ p^{r-1} \ zz $。我们利用滑动奇偶校验检查矩阵的天然块Toeplitz结构来得出逐步的方法论，以获取给定损坏的代码字$ W $的可能代码字的列表，即，即最接近的代码字到$ w $。
A convolutional code $\C$ over $\ZZ[D]$ is a $\ZZ[D]$-submodule of $\ZZN[D]$ where $\ZZ[D]$ stands for the ring of polynomials with coefficients in $\ZZ$. In this paper, we study the list decoding problem of these codes when the transmission is performed over an erasure channel, that is, we study how much information one can recover from a codeword $w\in \C$ when some of its coefficients have been erased. We do that using the $p$-adic expansion of $w$ and particular representations of the parity-check polynomial matrix of the code. From these matrix polynomial representations we recursively select certain equations that $w$ must satisfy and have only coefficients in the field $p^{r-1}\ZZ$. We exploit the natural block Toeplitz structure of the sliding parity-check matrix to derive a step by step methodology to obtain a list of possible codewords for a given corrupted codeword $w$, that is, a list with the closest codewords to $w$.
