5 research outputs found
Optimality of Huffman Code in the Class of 1-bit Delay Decodable Codes
For a given independent and identically distributed (i.i.d.) source, Huffman
code achieves the optimal average codeword length in the class of instantaneous
code with a single code table. However, it is known that there exist
time-variant encoders, which achieve a shorter average codeword length than the
Huffman code, using multiple code tables and allowing at most k-bit decoding
delay for k = 2, 3, 4, . . .. On the other hand, it is not known whether there
exists a 1-bit delay decodable code, which achieves a shorter average length
than the Huffman code. This paper proves that for a given i.i.d. source, a
Huffman code achieves the optimal average codeword length in the class of 1-bit
delay decodable codes with a finite number of code tables
General form of almost instantaneous fixed-to-variable-length codes
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 -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.Comment: submitted to IEEE Transactions on Information Theory. arXiv admin
note: text overlap with arXiv:1607.07247 by other author