On the capacity and error-correcting codes of write-efficient memories

Write-efficient memories (WEMs) were introduced by Ahlswede and Zhang (1989) as a model for storing and updating information on a rewritable medium with cost constraints. We note that the research work of Justesen and Hoholdt (1984) on maxentropic Markov chains actually provide a method for calculating the capacity of WEM. By using this method, we derive a formula for the capacity of WEM with a double-permutation cost matrix. Furthermore, some capacity theorems are established for a special class of WEM called deterministic WEM. We show that the capacity of deterministic WEM is equal to the logarithm of the largest eigenvalue of the corresponding connectivity matrix, it is interesting to note that the deterministic WEM behaves like the discrete noiseless channels of Shannon (1948). By specializing our results, we also obtain some interesting properties for the maximization problem of information functions with multiple variables which are difficult to obtain otherwise. Finally, we present a method for constructing error-correcting codes for WEM with the Hamming distance as the cost function. The covering radius of linear codes plays an important role in the constructions.