Distribution matching is the process of invertibly mapping a uniformlydistributed input sequence onto sequences that approximate the output of adesired discrete memoryless source. The special case of a binary outputalphabet and one-to-one mapping is studied. A fixed-length distribution matcheris proposed that is optimal in the sense of minimizing the unnormalizedinformational divergence between its output distribution and a binarymemoryless target distribution. Upper and lower bounds on the unnormalizeddivergence are computed that increase logarithmically in the output blocklength $n$. It follows that a recently proposed constant compositiondistribution matcher performs within a constant gap of the minimal achievableinformational divergence.
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机译：分布匹配是将均匀分布的输入序列可逆映射到近似所需离散无记忆源输出的序列的过程。研究了二进制输出字母和一对一映射的特殊情况。提出了一个固定长度的分布匹配器，从最小化其输出分布和无二进制内存目标分布之间的非标准化信息差异的角度来看，这是最佳的。计算未归一化散度的上限和下限，其在输出块长度$ n $中以对数形式增加。因此，最近提出的恒定组成分布匹配器在最小可达到的信息差异的恒定间隙内执行。
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