Error-correcting codes for ternarycontent addressable memories: A new perspective

Introduction: In the work "Error-Correcting Codes for Ternary Content Addressable Memories", Krishnan et al. show that under certain assumptions, using 2t + 1 copies of a word is an optimal strategy for guaranteeing the reliable operation of a ternary content addressable memory in the presence of up to t errors. Purpose: To present a new proof of the results of Krishnan et al. about coding for ternary content addressable memories and to extend these results somewhat. Results: A new logic-oriented extension of the Hamming distance is presented. Making use of this new distance, an alternate proof that repetition-based coding is optimal over the set of non-context-oriented codes is provided. The new proof allows the results of Krishnan et al. to be extended to cases where some information about the memory organization is available to the code designer. It is shown, for example, that the number of necessary redundancy bits in a non-context-oriented code cannot be reduced by assuming that the memory organizer stores codes in a particularly effective order. Practical relevance: The results described in this paper make clear that a repetition code is the optimal code for protecting the data stored in a ternary content addressable memories from errors. The new proof presented in this paper allows the results of Krishnan et al. to be extended to certain cases where some information about the memory organization is available to the code designer.