This paper presents an optimal construction of $N$-bit-delay almost instantaneous fixed-to-variable-length (AIFV) codes, the general form of binary codes we can make when finite bits of decoding delay are allowed. The presented method enables us to optimize lossless codes among a broader class of codes compared to the conventional FV and AIFV codes. The paper first discusses the problem of code construction, which contains some essential partial problems, and defines three classes of optimality to clarify how far we can solve the problems. The properties of the optimal codes are analyzed theoretically, showing the sufficient conditions for achieving the optimum. Then, we propose an algorithm for constructing $N$-bit-delay AIFV codes for given stationary memory-less sources. The optimality of the constructed codes is discussed both theoretically and empirically. They showed shorter expected code lengths when $N\ge 3$ than the conventional AIFV-$m$ and extended Huffman codes. Moreover, in the random numbers simulation, they performed higher compression efficiency than the 32-bit-precision range codes under reasonable conditions.

翻译：本文提出了一种N比特延迟几乎瞬时定长到变长码的最优构造方法，这是在允许有限比特解码延迟时所能构建的二进制码的一般形式。与传统的FV码和AIFV码相比，所提出的方法使我们能够在更广泛的码类中优化无损编码。本文首先讨论了码构造问题，该问题包含一些本质性的子问题，并定义了三种最优性类别，以阐明我们能在多大程度上解决这些问题。文章从理论上分析了最优码的性质，给出了达到最优的充分条件。随后，我们提出了一种针对给定平稳无记忆信源构造N比特延迟AIFV码的算法。从理论和实验两方面讨论了所构造码的最优性。结果表明，当N≥3时，其期望码长比传统的AIFV-m码和扩展霍夫曼码更短。此外，在随机数模拟中，在合理条件下，其压缩效率优于32位精度的区间码。