We propose a novel scheme for rate-compatible arbitrary-length polar code construction for the additive white Gaussian noise (AWGN) channel. The proposed scheme is based on the concept of non-uniform channel polarization. The original polar codes can only be designed with code lengths that are powers of two. Puncturing, shortening and extension are three strategies to obtain arbitrary code lengths and code rates for polar codes. There are other ways to design codes with arbitrary length but which have encoding and decoding with higher complexity such as multi-kernel, concatenated codes and specific constructions for Belief propagation (BP) or Successive Cancellation (SC) decoding. In general, the quality of the projected bit channels by these arbitrary-length techniques differs from that of the original bit channels, which can greatly affect the performance of the constructed polar codes. The proposed Non-Uniform Polarization based on Gaussian Approximation (NUPGA) is an efficient construction technique for rate-compatible arbitrary-length polar codes, which chooses the best channels (i.e., selects the positions of the information bits) by re-polarization of the codeword with desired length. A generalization of the Gaussian Approximation is devised for both polarization and re-polarization processes. We also present shortening and extension techniques for design polar codes. Simulations verify the effectiveness of the proposed NUPGA designs against existing rate-compatible techniques.
翻译:我们为添加白高斯噪声(AWGN)频道提出了一个与费率相匹配的任意长极代码构建新方案。拟议方案以非统一化频道极化概念为基础。原始极地代码只能设计为两种功率的代号长度。标定、缩短和扩展是获得任意性代码长度和极地代码率的三个战略。还存在其他任意长度设计代码的方法,但编码和解码的复杂程度更高,如多核心、融合型代码和信仰传播(BP)或成功取消(SC)解码的具体构件。一般来说,这些任意性长技术所预测的比特频道的质量与原始的比特频道不同,这可能会极大地影响已构建的极地代码的性能。基于高斯亚吸附法(NUPGA)的拟议非统一极地极化是一种高效的构建技术,它选择最佳渠道(i.e.e.,选择使用这些任意性长度技术预测的比特频道的质量频道的质量,并选择用于当前通用的平面代码的平面设计流程。我们目前选择的平级的平级的平级规则的比的平级结构的变的升级,这是目前对版版的平级的平极化,用来的平极地规则的平级的平级的平级的平极化,用来选择了目前设计设计设计设计流程的平比的平级的平比的平级的平极化。