基于广义生成矩阵的实用极化码构造
Practical Polar Code Construction Using Generalised Generator Matrices
摘要：
极化编码是最近提出的可以可证明地实现信道容量的编码技术。基于原始2x2生成器矩阵的极化码结构极化信道，即，一部分信道容量接近1，而剩余的信道容量接近0。由于该原始生成矩阵的特定大小，极化码只能具有等于2的幂的码长度，导致实际长度的码的效率低下。本文分析了有限长极化码在二进制擦除信道下的性能。一个归一化的极化距离测量的定义和极化码从不同的生成器矩阵显示不同的极化量进行比较，使用此措施。这些广义极化码的编码结构的建议和极化性能的渐近和有限长度的情况下进行了研究的大小为3x3和4x4的生成矩阵。一个广义的解码器也提出了这个生成矩阵和它的擦除率与原来的生成矩阵进行比较。研究表明，使用广义生成矩阵，可以构造性能与原始构造相似的极化码，并用于各种码长，不一定等于2的幂。
英文摘要：
Polar coding is a recently proposed coding technique that can provably achieve the channel capacity. The polar code structure, which is based on the original 2x2 generator matrix, polarises the channels, i.e., a portion of the channel capacities approach 1, while the remaining channel capacities approach 0. Due to the specific size of this original generator matrix, polar codes can only have code lengths equal to the powers of 2, resulting in inefficiency for codes of practical lengths. In this paper, the performance of finite-length polar codes over the binary erasure channel is analysed. A normalised polarisation distance measure is defined and polar codes from different generator matrices showing different amount of polarisation are compared using this measure. Encoding structures for these generalised polar codes are proposed and polarisation performances in both asymptotical and finite-length cases are investigated for generator matrices of size 3x3 and 4x4. A generalised decoder is also proposed for this generator matrix and its erasure rate is compared with that of the original generator matrix. It is shown that polar codes that have performance similar to the original construction can be constructed and used for a variety of code lengths, not necessarily equal to powers of 2, using generalised generator matrices.
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