Error-Pattern-Correcting Cyclic Codes Tailored to a Prescribed Set of Error Cluster Patterns

A new class of cyclic codes is discussed which is highly tailored to a prescribed set of dominant error cluster patterns. The cyclic code construction is based on a generator polynomial that produces a distinct syndrome set for each error pattern in the target set. By tailoring the generator polynomial specifically to the set of dominant error patterns, the code becomes highly effective in handling single and multiple occurrences of dominant error patterns at a very high code rate. A list decoding strategy based on a set of test word-error events is developed for the proposed codes, which efficiently utilizes both the algebraic information from the captured syndrome and the reliability measures provided by the local correlators matched to the dominant error patterns. By forcing a decoder to correct a single-pattern event for each test input word, multiple decoders running in parallel on the list of test words can effectively correct multiple error-pattern occurrences within the channel detector output word.