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      Use of Set Shaping theory in the development of locally testable codes

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      research-article
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      ScienceOpen Preprints
      ScienceOpen
      Set Shaping Theory, Information theory, Entropy, Data compression
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            Abstract

            Abstract: in developing locally testable codes, information is added to the coded message by creating redundancy in the codewords. In this article, we propose an alternative method in which redundancy is introduced on the message that must be transmitted before its encoding and not in the codewords. This approach exploits the Set Shaping Theory whose goal is the study the bijection functions f(X)=Y that transform a set of strings into a set of equal size made up of strings of greater length. In this way, this type of function transforms the independent variable x into the dependent variable y whose emission probability is conditioned by the previously emitted variables. Thus, if the decoder decodes a symbol associated with a conditional probability equal to zero, we detect an error in the message. If the function f used is the one that minimizes the average information content, we develop a code that can be tested efficiently. In fact, it is observed, in terms of compression, that the greater length of the strings is compensated by the fact of having chosen the strings with less entropy.

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            Author and article information

            Journal
            ScienceOpen Preprints
            ScienceOpen
            26 February 2022
            Affiliations
            [1 ] not affiliate
            Author notes
            Article
            10.14293/S2199-1006.1.SOR-.PPFVXSU.v1
            fc8d5cee-e459-429c-8b1d-2e07f10a2b7c

            This work has been published open access under Creative Commons Attribution License CC BY 4.0 , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Conditions, terms of use and publishing policy can be found at www.scienceopen.com .


            All data generated or analysed during this study are included in this published article (and its supplementary information files).
            Communication networks,Theoretical computer science,Applied computer science,Information systems & theory,General mathematics,General computer science
            Set Shaping Theory,Information theory,Entropy,Data compression

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