On a decoding algorithm by superposition for binary cyclic codes for certain burst errors

Cyclic codes are often used for the purpose of correcting burst errors in digital transmission and recording systems. Since the implementations of the encoding and syndrome calculations of these codes are simple, these codes have superior properties from a practical perspective. In this paper, an effective decoding method is given for certain burst errors (multiple solid-burst errors) that are contained within the detected errors resulting from a binary cyclic “predecoding” proces, where the precoding process for burst error correction is terminated at the detection stage. Such burst errors can be expressed as random errors by superimposing a copy of itself that has been cyclically shifted by one bit. So, by performing random error decoding on a version of the received sequence that has been superimposed with a one-bit cyclically shifted copy of itself, burst errors can be accurately corrected. This decoding method completely preserves the correction capacity of the precode and is applicable to any binary cyclic code with a minimum distance of at least 5. the correctable multiple solid-burst errors depend on the minimum distance of the code. Furthermore, by applying this technique to interleaved random error-correction codes for the purpose of correcting burst errors, it is shown that it is possible to extend the length of correctable burst errors.