On error detection and error synchronization of reversible variable-length codes

Reversible variable-length codes (RVLCs) are not only prefix-free but also suffix-free codes. Due to the additional suffix-free condition, RVLCs are usually nonexhaustive codes. When a bit error occurs in a sentence from a nonexhaustive RVLC, it is possible that the corrupted sentence is not decodable. The error is said to be detected in this case. We present a model for analyzing the error detection and error synchronization characteristics of nonexhaustive VLCs. Six indices, the error detection probability, the mean and the variance of forward error detection delay length, the error synchronization probability, the mean and the variance of forward error synchronization delay length are formulated based on this model. When applying the proposed model to the case of nonexhaustive RVLCs, these formulations can be further simplified. Since RVLCs can be decoded in backward direction, the mean and the variance of backward error detection delay length, the mean and the variance of backward error synchronization delay length are also introduced as measures to examine the error detection and error synchronization characteristics of RVLCs. In addition, we found that error synchronization probabilities of RVLCs with minimum block distance greater than 1 are 0.