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 $N$-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.Comment: submitted to IEEE Transactions on Information Theory. arXiv admin note: text overlap with arXiv:1607.07247 by other author

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

Développement d'une nouvelle technique de compression pour les codes variables à fixes quasi-instantanés

Pas toutes les techniques de compression des données adoptent le principe de dictionnaire pour représenter ses mots de code. Le dictionnaire est un ensemble de mots de code associés aux symboles sources lors de l’opération d’encodage. La correspondance entre le mot de code et le symbole source dépend de l’algorithme de compression adopté. Généralement, chaque algorithme construit son dictionnaire selon un ensemble de propriétés. Parmi ces propriétés nous avons celle de préfixe. Elle est primordiale pour les codes de type fixe à variable (FV) tels que l’algorithme de Huffman et celui de Shannon-Fano. Par contre, la propriété préfixe est optionnelle pour les codes de longueur variable à fixe (VF). Donc cela peut causer le but de pouvoir construire un dictionnaire plus performant, comme le cas des codes quasi-instantanés. Dans cette optique, Yamamoto et Yokoo ont éliminé cette condition pour créer un dictionnaire meilleur que celui de Tunstall. Les dictionnaires proposés par Yamamoto et Yokoo sont appelés les codes VF quasi-instantanés ou en anglais almost instantaneous VF codes. En s’appuyant sur leurs contributions, nous avons déduit que leur technique peut fournir dans certains cas des codes variables à fixes sous-optimaux, d’où notre suggestion de correctifs à leurs algorithmes pour en améliorer l’efficacité. Aussi nous proposons un autre mécanisme pour construire des codes VF en utilisant le principe de la programmation dynamique.Various techniques of data compression use a dictionary to represent their codewords. A dictionary is a set of codewords associated with the source symbols during the encoding operation. The correspondence between the codeword and the symbol source depends on the compression algorithm. Usually, the prefix property is key for the fixed-to-variable type codes FV as demonstrated in the Huffman and the Shannon-Fano algorithms. However, such a property may be eliminated for fixed-length codes in order to build a more efficient dictionary. In this context, Yamamoto and Yokoo excluded this condition to create a dictionary better than Tunstall. This new dictionary is called instantaneous variable-to-fixed code. Based on their contributions, we have deduced that their technique can provide, in some cases, suboptimal variable-to-fixed codes. Hence, we suggested to improve their algorithms. Also, we proposed another mechanism for building optimal AIVF codes by adopting the principle of dynamic programming