Performance of Error-Correcting Codes on Channels with Memory

Most magnetic recording and many other digital communication channels exhibit statistical dependencies among errors. The design of error-control schemes for such channels .requires proper models and tools that can be used to evaluate error performance after decoding. In this paper a simplified partitioned model of a channel with memory suggested by B. D. Fritchman is considered. This model is used to derive expressions for block and bit error probability bounds for major block burst-error-correcting codes: interleaved, single burst-correcting, and nonbiuary codes. The model-based bounds are compared to the experimental ones using the data obtained for helical scan magnetic tape recorders. The comparison showed an agreement between experimental and analytical data within one order of magnitude, with the average difference being as small as 16 percent in some cases. A simple and effective implementation of a multiple burst-error-correcting scheme based on the majority-logic decoding of interleaved binary codes is suggested. The scheme requires about ten off-the-shelf IC's for both encoder and decoder with the interleaving degree up to 512.