Abstract

ABSTRACT Huffman Compression, also known as Huffman Coding, is one of many compression techniques in use today. The two important features of Huffman coding are instantaneousness that is the codes can be interpreted as soon as they are received and variable length that is a most frequent symbol has length smaller than a less frequent symbol. The traditional Huffman coding has two procedures: constructing a tree in O(n 2 ) and then traversing it in O(n). Quantum computing is a promising approach of computation that is based on equations from Quantum Mechanics. Instantaneousness and variable length features are difficult to generalize to the quantum case. The quantum coding field is pioneered by Schumacher works on block coding scheme. To encode N signals sequentially, it requires O(N 3 ) computational steps. The encoding and decoding processes are far from instantaneous. Moreover, the lengths of all the codewords are the same. A Huffman-coding-inspired scheme for the storage of quantum information takes O(N(log N) a ) computational steps for a sequential implementation on non-parallel machines. The proposed algorithm, Quantum-inspired Huffman coding of symbols with equal frequencies, also has two procedures : calculating a quantum system state in O(n (lg n) 2 ) and then multiplying it by the inputs in O((lg n) 2 ). Finally, we present an unprecedented scheme for direct mapped Huffman codes that is O(lg n).