Worst-case Redundancy of Optimal Binary AIFV Codes and Their Extended Codes
Worst-case Redundancy of Optimal Binary AIFV Codes and Their Extended Codes
复制标题
最优二进制AIFV码及其扩展码的最坏情况冗余
DOI：
10.1109/tit.2017.2694017
复制
发表时间：
2016
影响因子：
2.5
通讯作者：
J. Honda
中科院分区：
文献类型：
--
作者：
Weihua Hu;Hirosuke Yamamoto;J. Honda
二进制几乎瞬时的固定到变量长度（AIFV）代码是无损代码，可以推广瞬时固定到可变长度代码的类别。该代码使用两个代码树，并分配源符号来不完整的内部节点和叶子。从经验上证明，AIFV代码比Huffman代码获得更好的压缩比。然而，最佳二进制AIFV代码的冗余上的上限仅为1，与Huffman代码的结合相同。在本文中，上限提高到1/2，这表明与代码最差的案例冗余相吻合。随之而来的是，最差的案例冗余是针对<inline-formula> <tex-math notegy =“ latex'> $ p _ {\ max} \ geq 1 $ </tex-math> </inline-inline-formula的来源的来源。 >/2，其中<inline-formula> <tex-math notege =“ latex”> $ p _ {\ max} $ </tex-math> </inline-formula>是最可能的源符号的概率。此外，我们提出了二进制AIFV代码的扩展，该代码使用<inline-formula> <tex-math notegy =“ latex”> $ m $ </tex-math> </inline-formula>代码树，最多允许<inline-formula> <Tex-Math notege =“ latex”> $ m $ </tex-math> </inline-formula> - 位解码延迟。我们表明，扩展二进制AIFV代码的最坏情况是<inline-formula> <tex-math notegy =“ latex”> $ 1/m $ </m $ </tex-math> </inline-formula> <inline-formula>公式> <tex-math notegy =“ latex”> $ m \ leq 4 $ </tex-math> </inline-formula>。
Binary almost instantaneous fixed-to-variable length (AIFV) codes are lossless codes that generalize the class of instantaneous fixed-to-variable length codes. The code uses two code trees and assigns source symbols to incomplete internal nodes as well as to leaves. AIFV codes are empirically shown to attain better compression ratio than Huffman codes. Nevertheless, an upper bound on the redundancy of optimal binary AIFV codes is only known to be 1, which is the same as the bound of Huffman codes. In this paper, the upper bound is improved to 1/2, which is shown to coincide with the worst-case redundancy of the codes. Along with this, the worst-case redundancy is derived for sources with <inline-formula> <tex-math notation="LaTeX">$p_{\max }\geq 1$ </tex-math></inline-formula>/2, where <inline-formula> <tex-math notation="LaTeX">$p_{\max }$ </tex-math></inline-formula> is the probability of the most likely source symbol. In addition, we propose an extension of binary AIFV codes, which use <inline-formula> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula> code trees and allow at most <inline-formula> <tex-math notation="LaTeX">$m$ </tex-math></inline-formula>-bit decoding delay. We show that the worst-case redundancy of the extended binary AIFV codes is <inline-formula> <tex-math notation="LaTeX">$1/m$ </tex-math></inline-formula> for <inline-formula> <tex-math notation="LaTeX">$m \leq 4$ </tex-math></inline-formula>.
几乎瞬时的 FV 代码
DOI：
--
发表时间：
2013
期刊：
影响因子：
--
作者：
土橋将人;山本博資;本多淳也;H.Yamamoto and X. Wei
通讯作者：
H.Yamamoto and X. Wei