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.
翻译:近年来,人们重新关注了算术编码(AC),这要归功于使用AC用于分配匹配(DM)以控制概率振幅成形的频道输入分布。AC固有的两个主要问题是:(1) 其所需的计算精度随着输入长度的线性增长,和(2) 需要高精度的乘数和分数。在这里,我们通过三个外观表(LUTs)引入了一种无倍化的AC-DM技术,解决上述两个问题。这些LUT用于通过增减来接近高精度乘数和分数。我们的方法所要求的精确度显示与输入长度的逻辑增长。我们证明,这种近似技术保持了DMD的不可忽略性。在1024符号的输入长度下,拟议的技术在全精度DM上损失了微不足道的速率(<0.01兆位/sym),同时需要少于4千字节的储存量。