The burst-trapping error control technique developed by Tong [1] corrects both random and burst errors adaptively. A generalization of this scheme, called generalized burst trapping (GBT), is presented here. Generalized burst-trapping codes (GBTC) also correct both random and burst errors adaptively but, in addition, are capable of correcting random errors in the guard space following a correctable burst. This added capability is obtained at the expense of a longer guard space or a lower rate and a modest increase in complexity of implementation. Nevertheless, these codes are simple to encode and decode and, in particular, the storage-saving technique used with the original burst-trapping codes is directly applicable to the generalized codes. Also it is shown that at most one block of error propagation can occur if a simple and reasonable condition is met. Thus the generalized codes have better propagation properties than the original burst-trapping codes. This new error control technique is well suited to error correction on channels where it cannot be assumed that bursts are isolated events separated by error-free intervals. Thus, for example, this technique appears well suited to error correction on telephone facilities that incorporate multiple-level signaling.

A systematic procedure for constructing binary self-orthogonal diffuse codes is presented. These codes correct both random and burst errors. A lower bound on actual constraint length for this class of codes is found. The given construction procedure generally yields codes that approach the lower bound for large burst error correction and are, therefore, asymptotically optimal.

It is shown that every linear cyclicb-burst-error-correcting code over any finite field can be modified to correct up to(b-2)symbols of synchronization slippage without additional redundancy, while maintaining its additive error-correcting capability in the absence of synchronization errors. For codes that are interleaved to a degreem, the synchronization error-correcting capability ism (b-1) - 1symbols, whereb \geq 3is the length of the burst each subcode corrects. This technique gives an optimum burst-error-correcting code a synchronization error-corecfing capability that is only one symbol short of the known upper bound and is hence asymptotically optimal. Moreover, the implementation is very simple.

An adaptive decoding technique called burst trapping is presented to correct both random and burst errors. Two decoding algorithms are used, one for random errors, and the other for bursts. The former is based on a conventional correction technique, the latter utilizes an encoding procedure for which each information digit appears twice in the data stream, first unchanged, and second combined with (addition modulo2) a check digit of a widely separated later block. Whenever the number of errors within a code block are detected to be too large to correct with the random-error-correcting algorithm, the burst-correcting algorithm corrects these errors by recovering the information from later blocks where it appears in combination with check digits. It is shown that the scheme requires very limited guard space and has limited error propagation. Furthermore, the storage requirement is even smaller than the guard space. This is the only known coding system that has this desirable feature. Results of simulation of such codes over telephone channels indicate that the performance of such codes, when compared with interleaved block codes, offers better results at significantly lower cost.