CRC Error Probability under Batch Random Noise

Abstract

We consider error probabilities in protocols using CRC to detect distortions in transmitted batches. A probability-theory model of an additive long-term noise is constructed as a sequence of independent noise blocks of a prescribed length. We show that there are conditions to be imposed on the form of the k-order polynomial forming the CRC and on block size s such that the error probability \(\alpha \) is close to \({{2}^{{ - k}}}\) and does not depend on s provided that distortion probability \({{P}_{1}}\) is high.