Capacity-achieving rate-compatible polar codes
Capacity-achieving rate-compatible polar codes
复制标题
DOI：
10.1109/isit.2016.7541257
复制
发表时间：
2015-10
期刊：
影响因子：
--
通讯作者：
Songnam Hong;D. Hui;I. Marić
中科院分区：
文献类型：
--
作者：
Songnam Hong;D. Hui;I. Marić
我们提出了一种构造速率兼容的极化码的方法，该极化码具有低复杂度的顺序解码器的容量实现。所提出的码构造允许以不同速率进行增量重传，以便适应信道条件。该构造的主要思想利用了极化码的某些共同特性，这些特性针对降级信道序列进行了优化。所提出的方法允许在每次传输时使用优化的极化码，从而实现容量。由于常规极化码的长度限制，所提出的构造仅能够支持受限的速率集合，当使用常规极化码时，受限的速率集合的特征在于核的大小。因此，我们考虑打孔极化码，其通过控制打孔分数在块长度上提供更大的灵活性。我们证明了任何给定的打孔分数的容量实现打孔极化码的存在。使用打孔极化码作为组成码，我们表明，所提出的速率兼容的极化码是容量实现的任意序列的速率和任何类的退化信道。
We present a method of constructing rate-compatible polar codes that are capacity-achieving with low-complexity sequential decoders. The proposed code construction allows for incremental retransmissions at different rates in order to adapt to channel conditions. The main idea of the construction exploits certain common characteristics of polar codes that are optimized for a sequence of degraded channels. The proposed approach allows for an optimized polar code to be used at every transmission thereby achieving capacity. Due to the length limitation of conventional polar codes, the proposed construction can only support a restricted set of rates that is characterized by the size of the kernel when conventional polar codes are used. We thus consider punctured polar codes which provide more flexibility on block length by controlling a puncturing fraction. We show the existence of capacity-achieving punctured polar codes for any given puncturing fraction. Using punctured polar codes as constituent codes, we show that the proposed rate-compatible polar code is capacity-achieving for an arbitrary sequence of rates and for any class of degraded channels.