Construction of high rate T-direct codes

• Published in: Computational & applied mathematics 2018-11, Vol.37 (5), p.5844-5856
• Main Authors: Devi, Meenakshi, Durai, R. S. Raja, Xu, Hongjun
• Format: Article
• Language: English
• Subjects: Applications of Mathematics; Applied physics; Codes; Coding; Computational mathematics; Computational Mathematics and Numerical Analysis; Constituents; Decoding; Mathematical Applications in Computer Science; Mathematical Applications in the Physical Sciences; Mathematics; Mathematics and Statistics
• ISSN: 0101-8205; 2238-3603; 1807-0302
• DOI: 10.1007/s40314-018-0665-8

This paper presents a class of multi-user codes named as T - direct tertiary codes. These classes of codes have higher information rate in comparison to the existing T - direct codes. A coding scheme (encoding and decoding) is proposed for the class of T - direct codes, that increases the information rate of the constituent codes in comparison to the existing coding scheme for the class of T - direct codes: the coding scheme first drives the code C i ′ ( n ′ , k ′ , d ′ ) from the constituent code C i ( n , k , d ) of existing T - direct code ( C 1 , C 2 , … , C T ) with k ′ n ′ ≥ k n , and eventually forms a T - direct code ( C 1 ′ , C 2 ′ , … , C T ′ ) with an overall increase in sum-rate. Just like T - direct codes, the newly constructed class of codes can be used for simultaneous transmission of non-binary symbols over an F -adder channel. Further, an associated decoding technique for the constructed class of codes is also proposed.