Communication Control and Signal Processing Seminar: Jie Li, "Systematic Constructions of MDS Codes"
Communication, Control and Signal Processing Seminar
Systematic Constructions of MDS Codes with Small Sub-packetization Level and Near Optimal Repair Bandwidth
Southeast Jiaotong University
In the literature, all the known high-rate MDS codes with the optimal repair bandwidth possess a significantly large sub-packetization level, which may prevent the codes to be implemented in practical systems. To build MDS codes with small sub-packetization level, existing results and the theoretical bounds imply that one may sacrifice the optimality of the repair bandwidth.
In this talk, we present a powerful transformation that can greatly reduce the sub-packetization level of the any MDS codes with respect to the same code length $n$, then followed by three applications of the transformation, where three high-rate MDS codes that have both small sub-packetization level and near optimal repair bandwidth can be obtained, however, over a sufficiently large finite field. To further reduce the field size, we also propose two explicit $(n=sn',k)$ MDS codes that have both small sub-packetization level and near optimal repair bandwidth, where the size $q$ of the finite fields required are respectively reduced to $q>n$ and $q>s(n-k)$.