  Despite the great promises that the resistive random access memory (ReRAM)
has shown as the next generation of non-volatile memory technology, its
crossbar array structure leads to a severe sneak path interference to the
signal read back from the memory cell. In this paper, we first propose a novel
belief propagation (BP) based detector for the sneak path interference in
ReRAM. Based on the conditions for a sneak path to occur and the dependence of
the states of the memory cells that are involved in the sneak path, a Tanner
graph for the ReRAM channel is constructed, inside which specific messages are
updated iteratively to get a better estimation of the sneak path affected
cells. We further combine the graph of the designed BP detector with that of
the BP decoder of the polar codes to form a joint detector and decoder.
Tailored for the joint detector and decoder over the ReRAM channel, effective
polar codes are constructed using the genetic algorithm. Simulation results
show that the BP detector can effectively detect the cells affected by the
sneak path, and the proposed polar codes and the joint detector and decoder can
significantly improve the error rate performance of ReRAM.
