The purpose of this paper is to organize and clarify the work of the past decade on burst-correcting codes. Our method is, first, to define an idealized model, called the classic bursty channel, toward which most burst-correcting schemes are explicitly or implicitly aimed; next, to bound the best possible performance on this channel; and, finally, to exhibit classes of schemes which are asymptotically optimum and serve as archetypes of the burstcorrecting codes actually in use. In this light we survey and categorize previous work on burst-correcting codes. Finally, we discuss qualitatively the ways in which real channels fail to satisfy the assumptions of the classic bursty channel, and the effects of such failures on the various types of burst-correcting schemes. We conclude by comparing forward-error-correction to the popular alternative of automatic repeat-request (ARQ).

Burst-Correcting Codes for the Classic Bursty Channel

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 modulo 2 ) 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.

Burst-trapping techniques for a compound channel

Modern hi-tech systems rely heavily on communication networks while operating in increasingly harsher electromagnetic conditions. To protect transmitted data from corruption, Error Correcting Codes are widely used. In this paper, the effectiveness of the Hamming code is evaluated under harsh electromagnetic disturbances. Our simulations show that, under certain conditions, the impact of the introduced overhead cannot be compensated by the single error correcting capabilities of the Hamming codes. Moreover, for specific bit and disturbance frequencies and for larger data sets, the use of a Hamming code provides limited to no advantage.

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Effectiveness of Hamming Single Error Correction Codes Under Harsh Electromagnetic Disturbances

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.

Systematic construction of self-orthogonal diffuse codes

In Cooperative Intelligent Transportation Systems (C-ITSs), vehicles need to wirelessly connect with Roadside units (RSUs) over limited durations when such point-to-point connections are possible. One example of such communications is the downloading of maps to the C-ITS vehicles. Another example occurs in the testing of C-ITS vehicles, where the tested vehicles upload trajectory records to the roadside units. Because of real-time requirements, and limited bandwidths, data are sent as User Datagram Protocol (UDP) packets. We propose an inter-packet error control coding scheme that improves the recovery of data when some of these packets are lost; we argue that the coding scheme has to be one of convolutional coding. We measure performance through the session averaged probability of successfully delivering groups of packets. We analyze two classes of convolution codes and propose a low-complexity decoding procedure suitable for network applications. We conclude that Reed–Solomon convolutional codes perform better than Wyner–Ash codes at the cost of higher complexity. We show this by simulation on the memoryless binary erasure channel (BEC) and channels with memory, and through simulations of the IEEE 802.11p DSRC/ITS-G5 network at the C-ITS test track AstaZero.

Low Delay Inter-Packet Coding in Vehicular Networks

We derive a new family of convolutional character-error-correcting codes which are a convolutional form of the Reed-Solomon block codes and as such have nonbinary symbols. We also derive a bound on the error correcting capabilities of these codes in which the error-correcting capability per constraint length grows approximately with the square root of the constraint length. When these codes are used on a binary channel they are effective for both random and burst error correction because a single character spans several channel digits. These codes have greater error-correcting capabilities than the Robinson-Bernstein self-orthogonal codes but are harder to decode. The single-character-error-correcting codes, when interleaved, are shown to be more powerful than the equivalent Hagelbarger code and appear to be simpler to implement. They are also slightly better than the interleaved version of Berlekamp's code. We discuss encoding and decoding algorithms and illustrate a simple decoding algorithm for some of the codes. These codes are closely related to the Bose-Chaudhuri-Hocquenghem block codes and share with them the decoding simplification for character erasures in place of errors. Any Bose-Chaudhuri-Hocquenghem decoding algorithm can be used to decode these codes.

S. Y. Tong

Papers

Convolutional reed-solomon codes