Explicit capacity achieving codes for defective memories

The problem of constructing error correcting codes for defective memories, where some of the cells are defected and unable to switch their states, is considered. This is a classical problem in coding theory which has recently received renewed attention due to application to new technologies for non-volatile memories such as phase change memories. We show how the state of the art capacity achieving codes, in combination with a coset coding and another error correcting code, can be used in order to asymptotically achieve the capacity of the binary defective memory. The resulting schemes are explicit, have polynomial time encoder and quasilinear time decoder. The model is further generalized by considering erasures on top of the defective cells. We propose the partitioned polar codes for this model and prove that they achieve the capacity.