Protecting Multi-Level Memories from Jamming Using Q-ary Expurgated Robust Codes

Robust codes can effectively detect jamming in qq-ary memories for q=2tq=2t. When qq is not a power of two, a binary information word has to be converted into a qq-ary word prior to the encoding. This conversion expurgates the code since some of the qq-ary codewords are never used. Unless properly designed, expurgation can significantly degrade the effectiveness of the code in terms of its error detection capability. This article analyzes the error masking probability of an expurgated robust code when applied to qq-ary memories. It is shown that by wisely designing the converter, this degradation can be minimized, and in some cases, the code's efficiency can be superior to the original code.