Razane Tajeddine PhD Student Advisor Dr. Salim El Rouayheb - PowerPoint PPT Presentation

Razane Tajeddine PhD Student Advisor Dr. Salim El Rouayheb

Maximum Rank Distance (MRD) codes • I am currently in the beginning of my work. I’m interested in topics related to graph theory, coding theory and information theory. • I am reading the literature related to MRD codes. [Gabidulin, 1985] Classical Codes Rank Metric Codes Codewords Vectors Matrices Distance Hamming Rank(A-B) Code MDS MRD • Recent applications of MRD codes to secure network codes. [Silva et al, 2008]

Research Directions • Currently exploring the possibility of applying MRD codes to security in distributed storage systems (DSS), and index coding. Network representation of a distributed Index coding example storage system

MRD code Construction • 𝑣 1 , 𝑣 2 , … 𝑣 𝑂 is a basis of 𝐻𝐺 𝑟 𝑂 . • Performing a bijection for any element 𝑦 𝑗 ∈ 𝐻𝐺 𝑟 𝑂 to vector 𝑏 1𝑗 , 𝑏 2𝑗 , … 𝑏 𝑂𝑗 , where 𝑦 𝑗 = 𝑏 1𝑗 𝑣 1 + 𝑏 2𝑗 𝑣 2 +…+ 𝑏 𝑂𝑗 𝑣 𝑂 • The rank of vector x is the rank of the matrix 𝑏 11 𝑏 12 … 𝑏 1𝑂 𝑏 21 𝑏 22 … 𝑏 2𝑂 . . . . . . . . . 𝑏 𝑂1 𝑏 𝑂2 … 𝑏 𝑂𝑂 • Code rank distance is the rank of the difference between two vectors x and y, which generate the minimum rank distance. • MRD codes are (n,k)-codes that achieve the rank distance = 𝑜 – 𝑙 + 1 .