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

Razane Tajeddine

PhD Student

Advisor

• Dr. Salim El Rouayheb

• 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]

• Recent applications of MRD codes to secure network codes.

[Silva et al, 2008]

Maximum Rank Distance (MRD) codes

Classical Codes Rank Metric Codes Codewords Vectors Matrices Distance Hamming Rank(A-B) Code MDS MRD

• Currently exploring the possibility of applying MRD codes to

security in distributed storage systems (DSS), and index coding.

Network representation of a distributed storage system Index coding example

Research Directions

• 𝑣1, 𝑣2, … 𝑣𝑂 is a basis of 𝐻𝐺 𝑟𝑂 .
• Performing a bijection for any element 𝑦𝑗 ∈ 𝐻𝐺 𝑟𝑂 to vector

𝑏1𝑗, 𝑏2𝑗, … 𝑏𝑂𝑗, where 𝑦𝑗 = 𝑏1𝑗𝑣1 + 𝑏2𝑗𝑣2+…+𝑏𝑂𝑗𝑣𝑂

• The rank of vector x is the rank of the matrix

𝑏11 𝑏12 … 𝑏1𝑂 𝑏21

. . .

𝑏22

. . .

… 𝑏2𝑂

. . .

𝑏𝑂1 𝑏𝑂2 … 𝑏𝑂𝑂

• 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.

MRD code Construction