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Abstract
In coding theory, we study various properties of codes for application in data compression, cryptography, error correction, and network coding. The study of codes is introduced in Information Theory, electrical engineering, mathematics, and computer sciences for the transmission of data through reliable and efficient methods. We have to consider how coding of messages can be done efficiently so that the maximum number of messages can be sent over a noiseless channel in a given time. Thus, the minimum value of mean codeword length subject to a given constraint on codeword lengths has to be founded. In this paper, we have introduced mean codeword length of orderαand typeβfor 1:1 codes and analyzed the relationship between average codeword length and fuzzy information measures for binary 1:1 codes. Further, noiseless coding theorem associated with fuzzy information measure has been established.
Highlights
We have introduced mean codeword length of order α and type β for 1:1 codes and analyzed the relationship between average codeword length and fuzzy information measures for binary 1:1 codes
In the 1940s, a new branch of mathematics was introduced as Information Theory
Information Theory deals with the study that how information can be transmitted over communication channels
Summary
In the 1940s, a new branch of mathematics was introduced as Information Theory. Information Theory considered the problems of how to process information, how to store information, how to retrieve information, and decisionmaking. Gurdial and Pessoa [13] proved noiseless coding theorem by giving lower bounds for useful mean codeword lengths of order α in terms of useful measures of information of order α. Baig and Dar [14, 15] proposed a new considered fuzzy information measure of order α and type β: Hαβ (A; U) For this information measure they introduced the given mean code length of order α and type β: Lβα (U). Taneja and Bhatia [18] proposed a generalized mean codeword length for the best 1:1 code and Parkash and Sharma [19, 20] proved some noiseless coding theorems corresponding to fuzzy entropies and introduced a new class of fuzzy coding theorems. We will prove the fuzzy noiseless theorem for 1:1 codes of binary size and prove that they are less constrained
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