Multiple-burst-error correction by threshold decoding

A class of cyclic product codes capable of correcting multiple-burst errors is studied. A code of dimension p is constructed by forming the cyclic product of p one-dimensional single-parity-check codes of relatively prime block lengths. A consideration of the parity-check matrix shows that there are p orthogonal parity checks on each digit, and a burst of length b can corrupt at most one of the parity checks. The maximum allowable value of b can be easily calculated. The codes are completely orthogonal and [p/2] bursts of length b or less can be corrected by one-step threshold decoding.These codes have a very interesting geometric structure which is also discussed. Using the geometric structure, we show that the codes can also correct 2p−2 bursts of relatively short lengths. However, in this case the errors cannot be corrected by threshold decoding