1 research outputs found
Duality between erasures and defects
We investigate the duality of the binary erasure channel (BEC) and the binary
defect channel (BDC). This duality holds for channel capacities, capacity
achieving schemes, minimum distances, and upper bounds on the probability of
failure to retrieve the original message. In addition, the relations between
BEC, BDC, binary erasure quantization (BEQ), and write-once memory (WOM) are
described. From these relations we claim that the capacity of the BDC can be
achieved by Reed-Muller (RM) codes under maximum a posterior (MAP) decoding.
Also, polar codes with a successive cancellation encoder achieve the capacity
of the BDC.
Inspired by the duality between the BEC and the BDC, we introduce locally
rewritable codes (LWC) for resistive memories, which are the counterparts of
locally repairable codes (LRC) for distributed storage systems. The proposed
LWC can improve endurance limit and power efficiency of resistive memories.Comment: Presented at Information Theory and Applications (ITA) Workshop 2016.
arXiv admin note: text overlap with arXiv:1602.0120