Logical Implication to Reduce Run Time Memory Requirement and Searches During LZW Decompression

Abstract

LZW data compression algorithm maintains n distinct codes in dictionary for n distinct patterns in input string. Consequently, to decode a code, the decompressor unnecessarily searches over a set of n codes. We have presented a universal pattern encoding and decoding technique called MSED (Mother Saraswati Encoding and Decoding) in this work. MSED uses logical implication as a powerful tool to encode and decode patterns. We have proved that encoding patterns with logical implication achieve two improvements: (i) reduced memory requirement of LZW and (ii) reduced required number of searches in order to decode any code during decompression. In MSED technique, dictionary of the LZW compressor consists of an ordered pair of distinct patterns as (P_k, P_m) and code for P_k. Code of P_m is unambiguously determined from code of P_k using logical implication and complement operation. LZW decompressor dictionary has extra 2-bit information called recent to indicate the most recently entered pattern P_k or P_m. Hence, only $\frac{n}{2}$ codes to maintain for n patterns in dictionary. Thus, memory is saved and decompressor searches at most $\frac{n}{2}$ codes in order to decode any code.