Sparse Graphs for Belief Propagation Decoding of Polar Codes
Sparse Graphs for Belief Propagation Decoding of Polar Codes
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DOI：
10.1109/isit.2018.8437581
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发表时间：
2017-12
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通讯作者：
Sebastian Cammerer;Moustafa Ebada;Ahmed Elkelesh;S. Brink
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作者：
Sebastian Cammerer;Moustafa Ebada;Ahmed Elkelesh;S. Brink
我们描述了一种新的方法，将极地代码解释为具有基础稀疏解码图的低密度奇偶校验检查（LDPC）的代码。该稀疏图基于极地代码的编码因子图，适用于常规信念传播（BP）解码。我们讨论了基于检查节点解码器（CND）和可变节点解码器（VND）更新方程的几种修剪技术，从而大大降低了奇偶校验检查矩阵的大小（即解码复杂性）。结果，可以在稀疏图上进行迭代极性解码，类似于传统的良好的LDPC解码，例如，使用完全平行的Sum-Product算法（SPA）。这使用分析LDPC代码已知的知名工具促进了极地代码的系统分析和设计。我们表明，与Arikan的原始BP解码器相比，所提出的迭代极性解码器对于短期中间代码长的性能损失微不足道。最后，所提出的解码器被证明可以从降低的复杂性和减少的内存需求中受益，因此更适合于硬件实现。
We describe a novel approach to interpret a polar code as a low-density parity-check (LDPC)-like code with an underlying sparse decoding graph. This sparse graph is based on the encoding factor graph of polar codes and is suitable for conventional belief propagation (BP) decoding. We discuss several pruning techniques based on the check node decoder (CND) and variable node decoder (VND) update equations, significantly reducing the size (i.e., decoding complexity) of the parity-check matrix. As a result, iterative polar decoding can then be conducted on a sparse graph, akin to the traditional well-established LDPC decoding, e.g., using a fully parallel sum-product algorithm (SPA). This facilitates the systematic analysis and design of polar codes using the well-established tools known from analyzing LDPC codes. We show that the proposed iterative polar decoder has a negligible performance loss for short-to-intermediate codelengths compared to Arikan's original BP decoder. Finally, the proposed decoder is shown to benefit from both reduced complexity and reduced memory requirements and, thus, is more suitable for hardware implementations.