Log-CCDM：基于无乘法算术编码的分布匹配
Log-CCDM: Distribution Matching via Multiplication-free Arithmetic Coding
摘要：
近年来，算术编码（AC）重新受到关注。这是由于使用AC进行分布匹配（DM）以控制概率幅度整形中的通道输入分布。AC有两个固有的主要问题：（1）它所需的算术精度随着输入长度线性增长，以及（2）需要高精度的乘法和除法。在这里，我们介绍了一种无乘法AC为基础的DM技术，通过三个查找表（LUT），解决了上述两个问题。这些LUT用于通过加法和减法来近似高精度乘法和除法。所需的精度，我们的方法被证明与输入长度的几何增长。我们证明，这种近似技术保持DM的可逆性。在1024个符号的输入长度，所提出的技术实现了可忽略的速率损失（$<0.01$位/sym）对全精度DM，而需要小于4兆字节的存储。
英文摘要：
Recent years have seen renewed attention to arithmetic coding (AC). This is thanks to the use of AC for distribution matching (DM) to control the channel input distribution in probabilistic amplitude shaping. There are two main problems inherent to AC: (1) its required arithmetic precision grows linearly with the input length, and (2) high-precision multiplications and divisions are required. Here, we introduce a multiplication-free AC-based DM technique via three lookup tables (LUTs) which solves both problems above. These LUTs are used to approximate the high-precision multiplications and divisions by additions and subtractions. The required precision of our approach is shown to grow logarithmically with the input length. We prove that this approximate technique maintains the invertibility of DM. At an input length of 1024 symbols, the proposed technique achieves negligible rate loss ($<0.01$ bit/sym) against the full-precision DM, while requiring less than 4 kilobytes of storage.
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