Correction of faulty signal transmission for resilient designs of signed-digit arithmetic

When arithmetic components are parallelized, fault-prone interconnections can tamper results significantly. Advances in feature size shrinking lead to a steady increase of errors caused by faulty transmission. We suggest to employ resilient data encoding schemes to offset these negative effects. Focusing on parallel signed-digit based arithmetic, frequently used in highspeed systems, we found that a suitable data encoding can reduce error rates by about 25% when using 2-bit encoding and about 62% when using 3-bit encoding. Data encoding should be driven by symbol occurrence probabilities. We develop a methodology to obtain these probabilities, show example fault-tolerant encodings, and discuss the impact on communicating parallel arithmetic circuits in example error scenarios.