Index Coding from Reed-Solomon Codes

• DOI: 10.22533/at.ed.3173122324047

• Palavras-chave: Index Coding, Lateral Information, Error Correcting Codes, Finite Bodies.

• Keywords: Index Coding, Lateral Information, Error Correcting Codes, Finite Bodies.

• Abstract:

  The problem of index coding subject to transmission errors was initially considered by Dau et al. [5]. In this work we establish a connection between index coding and error correcting codes, through the tree construction for nested cyclic codes proposed in [3]. We implemented tree construction algorithms in the Matlab language, which help to solve some implementation problems found in [3]. We verified that for cyclic codes there will not always be an increase in the error correction capacity between the levels of the tree, which is why we restricted this study, initially, to Reed-Solomon codes, since they are MDS codes, which guarantees an increase in the distance of Hamming at each level. This means that, under certain conditions, knowledge of lateral information will be interpreted as an increase in the error correction capability of the decoder.