Merge source coding

We show that any comparison-based merging algorithm can be naturally mapped into a source coder via a conversion function introduced here. By applying this function over some well known merging algorithms, namely Binary Merging and Recursive Merging, we show that they are closely related to a runlength-based coder with Rice coding and to the Binary Interpolative Coder, respectively. Furthermore, by applying the conversion function over the Probabilistic Merging algorithm we obtain a runlength-based coder that uses a new variant of the Rice code, namely Randomized Rice Code. This new code uses a random source of bits with the aim of reducing its average redundancy.

[1]  Glen G. Langdon,et al.  Arithmetic Coding , 1979 .

[2]  Andrew Chi-Chih Yao,et al.  An Almost Optimal Algorithm for Unbounded Searching , 1976, Inf. Process. Lett..

[3]  Frank K. Hwang,et al.  A Simple Algorithm for Merging Two Disjoint Linearly-Ordered Sets , 1972, SIAM J. Comput..

[4]  Ian H. Witten,et al.  Lossless Compression for Text and Images , 1997 .

[5]  Peter Elias,et al.  Universal codeword sets and representations of the integers , 1975, IEEE Trans. Inf. Theory.

[6]  Robert F. Rice,et al.  Some practical universal noiseless coding techniques , 1979 .

[7]  Krzysztof Dudzinski,et al.  On a Stable Minimum Storage Merging Algorithm , 1981, Inf. Process. Lett..

[8]  C. Christen.  Improving the bounds on optimal merging , 1978, 19th Annual Symposium on Foundations of Computer Science (sfcs 1978).

[9]  Paul K. Stockmeyer,et al.  On the Optimality of Linear Merge , 1980, SIAM J. Comput..

[10]  Glenn K. Manacher,et al.  Significant Improvements to the Hwang-Lin Merging Algorithm , 1979, JACM.

[11]  Erik D. Demaine,et al.  Adaptive set intersections, unions, and differences , 2000, SODA '00.

[12]  Donald E. Knuth,et al.  The Art of Computer Programming: Volume 3: Sorting and Searching , 1998 .

[13]  Svante Carlsson,et al.  Sublinear merging and natural mergesort , 2005, Algorithmica.

[14]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[15]  Claire Mathieu,et al.  Alternation and redundancy analysis of the intersection problem , 2008, TALG.

[16]  Sampath Kannan,et al.  Two Probabilistic Results on Merging , 1993, SIAM J. Comput..

[17]  David A. Huffman,et al.  A method for the construction of minimum-redundancy codes , 1952, Proceedings of the IRE.

[18]  Alistair Moffat,et al.  Binary Interpolative Coding for Effective Index Compression , 2000, Information Retrieval.

[19]  Solomon W. Golomb,et al.  Run-length encodings (Corresp.) , 1966, IEEE Trans. Inf. Theory.