A Necessary and Sufficient Condition for the Existence of Asymmetrical Reversible VLCs
Richa Gupta1, Radhika Goel2

1Richa Gupta, Department of Electronics and Communication Engineering, JIIT, Noida (U.P), India.
2Radhika Goel, Department of Electronics and Communication Engineering, Krishna Engineering College, Ghaziabad (U.P), India.
Manuscript received on 05 February 2019 | Revised Manuscript received on 13 February 2019 | Manuscript published on 28 February 2019 | PP: 314-317 | Volume-8 Issue-4, February 2019 | Retrieval Number: D2789028419/19©BEIESP
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC-BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)

Abstract: Affix-free codes are widely used in multimedia communications because of its error tolerance capbility. Reversible Variable Length Code (RVLC) is a type of affix-free code. In literature, there are many construction algorithms available for RVLCs. But unlike Variable Length Codes (VLCs), RVLCs lack in the area of its mathematical development in the form of lower bound or upper bound on average codeword length, bounds on existence, and related Theorems. Only few mathematicians have done some work on this. In 2014, Richa and Radhika have proposed and discussed the necessary and sufficient condition on the number of codewords for a particular (bit length vector) required for the existence of symmetrical RVLCs. This paper is an extension of the earlier published paper on the similar ground, but for asymmetrical RVLCs. This paper derives and discusses necessary and sufficient condition, on bit length vector (the number of codewords for a particular length), required for the existence of asymmetrical RVLCs over the given D-ary code alphabet.
Keyword: Affix-Free Codes, Symmetrical RVLC, Asymmetrical Rvlcs, Mathematical Bound On RVLC, Bit Length Vector, Kraft Inequality.
Scope of the Article: Ubiquitous Multimedia Computing