General form of almost instantaneous fixed-to-variable-length codes and optimal code tree construction
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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 proposed codes, N-bit-delay AIFV codes, are represented by multiple code trees with high flexibility. The paper guarantees them to be uniquely decodable and present a code-tree construction algorithm under a reasonable condition. The presented algorithm provides us with a set of code trees, which achieves minimum expected code length, among a subset of N-bit-delay AIFV codes for an arbitrary source. The experiments show that the proposed codes can perform more efficiently compared to the conventional AIFV-m and Huffman codes. Additionally, in some reasonable cases, the proposed codes even outperform the 32-bit-precision range codes. The theoretical and experimental results in this paper are expected to be very useful for further study on AIFV codes.
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