A general class of the almost instantaneous fixed-to-variable-length (AIFV) codes is proposed, which contains every possible binary code we can make when allowing finite bits of decoding delay. The contribution of the paper lies in the following. (i) Introducing $N$-bit-delay AIFV codes, constructed by multiple code trees with higher flexibility than the conventional AIFV codes. (ii) Proving that the proposed codes can represent any uniquely-encodable and uniquely-decodable variable-to-variable length codes. (iii) Showing how to express codes as multiple code trees with minimum decoding delay. (iv) Formulating the constraints of decodability as the comparison of intervals in the real number line. The theoretical results in this paper are expected to be useful for further study on AIFV codes.

翻译：本文提出了一类广义的接近瞬时固定到变长（AIFV）码，涵盖了在允许有限比特解码延迟条件下所能构造的所有可能二进制码。本文的贡献在于：（i）引入了由多个具有比传统AIFV码更高灵活性的码树构建的$N$比特延迟AIFV码；（ii）证明了所提出的码能够表示任何唯一可编码且唯一可解码的变长到变长码；（iii）展示了如何以最小解码延迟将码表示为多个码树；（iv）将可解码性约束描述为实数轴上区间的比较。本文的理论结果有望为AIFV码的进一步研究提供参考。