On a simple method for detecting synchronization errors in coded messages

Abstract

Abstract-We investigate the problem of designing pairs ( ) of words with the property that, if each word of a coded message is prefixed by and suffixed by , the resulting set of coded messages is error detecting with finite delay. We consider (combinatorial) channels permitting any combination of the substitution, insertion, and deletion (SID) error types, and address the cases of both scattered and burst errors. A pair ( ) with the above property is evaluated in terms of three parameters: redundancy, delay of decoding, and frequency of the detectable errors. In the case of SID channels with burst errors, we provide a complete and explicit characterization of their error-detecting pairs ( ), which involves the period of the word .Index Terms-Burst errors, decoding delay, deletion, error detection, insertion, period of word.

Insertion/Deletion Detecting Codes and the Boundary Problem

“…The concept of insertion/deletion detecting codes is not novel, but seems to have been first introduced by Konstantinidis et al [11]. They construct non-binary codes capable of detecting various combinations of substitution, insertion and deletion errors.…”

“…They construct non-binary codes capable of detecting various combinations of substitution, insertion and deletion errors. Here, we will define insertion/deletion detecting codes in a slightly different manner to that by Konstantinidis et al [11]. We first give our definition of insertion/deletion detecting codes and the construction of such codes, and then highlight the differences between our codes and that of Konstantinidis et al [11] afterwards.…”

“…Konstantinidis et al [11] discovered a class of codes closely related to . As stated earlier in this section, our definition of insertion/deletion detecting codes is slightly different to theirs.…”

“…An equally fundamental topic is insertion/deletion detection. Konstantinidis et al [11] were the first to introduce insertion/deletion detecting codes. In this paper we will show how insertion/deletion detecting codes provide a different perspective on the boundary problem of number-theoretic codes.…”

“…In Section II, we introduce our definition of insertion/deletion detecting codes and demonstrate a simple systematic form of these codes. We also consider the differences and the similarities of these codes with the insertion/deletion detecting codes developed by Konstantinidis et al [11]. In Section III, we consider how insertion/deletion detecting codes can be utilised to overcome some aspects of the boundary problem.…”