Analysis and Practice of Uniquely Decodable One-to-One Code

• Main Authors: Liu, Chin-Fu, 劉勁甫
• Other Authors: Chen, Po-Ning
• Format: Others
• Language: en_US
• Published: 2013
• Online Access: http://ndltd.ncl.edu.tw/handle/99031796479112363191

碩士 === 國立交通大學 === 電信工程研究所 === 101 === In this thesis, we consider the so-called uniquely decodable one-to-one code (UDOOC) that is formed by inserting a “comma” indicator, termed the unique word (UW), between consecutive one-to-one codewords for separation. Along this research direction, we first investigate the general combinatorial properties of UDOOCs, in particular the enumeration of UDOOC codewords for any (finite) codeword length. Based on the obtained formula on the number of length-n codewords for a given UW, the average codeword length of the optimal UDOOC for a given source statistics can be computed. Upper bounds on the average codeword length of UDOOCs are next established. The analysis on bounds of the average codeword length then leads to two asymptotic bounds on ultimate per-letter average codeword length, one of which is achievable and hence tight for a certain source statistics and UW, and the other of which proves the achievability of source entropy rate of UDOOCs when both the block size of source letters for UDOOC compression and UW length go to infinity. Efficient encoding and decoding algorithms for UDOOCs are subsequently given. Numerical results show that when grouping three English letters as a block, the UDOOCs with UW = 0001, 0000, 000001 and 000000 can respectively reach the compression rates of 3.531, 4.089, 4.115 and 4.709 bits per English letter (with the lengths of UWs included), where the source stream to be compressed is the book titled Alice’s Adventures in Wonderland. In comparison with the first-order Huffman code, the second-order Huffman code, the third-order Huffman code and the Lembel-Ziv code, which respectively achieve the compression of 3.940, 3.585, 3.226 and 6.028 bits per single English letter, the proposed UDOOCs can potentially in comparable compression rate to the Huffman code under similar decoding complexity and yield a better average codeword length than that of the Lempel-Ziv code, thereby confirming the practicability of the simple idea of separating OOC codewords by UWs.