Report on models of write–efficient memories with localized errors and defects

Write–efficient memories (WEM) as a model for storing and updating information were introduced by R. Ahlswede and Z. Zhang [R. Ahlswede, Z. Zhang, Coding for write efficient memory, Inform. and Computation 83 (1) (1989) 80–97]. We consider now three new models of WEM with localized errors and defects, resp. situation ( E + , D − ), where the encoder is informed but the decoder is not informed about the previous state of the memory we study codes correcting defects, codes detecting localized errors. y, in the situation ( E + , D + ), where both, the encoder and the decoder, are informed about the previous state of the memory we study codes correcting localized errors. three cases we determine for binary alphabet the optimal rates under a cost constraint defined in terms of the Hamming distance.