Combined permutation codes for synchronization

Abstract: A combined code is a code that combines two or more characteristics of other codes. A construction is presented in this paper of permutation codes that are self-synchronizing and able to correct a number of deletion errors per codeword, thus a combined permutation code. Synchronization errors, modelled as deletion(s) and/or insertion(s) of bits or symbols, can be catastrophic if not detected and corrected. Some classes of codes have been proposed that are synchronizable, i.e. they can be used to regain synchronization although the error leading to the loss of synchronization is not corrected. Typically, different classes of codes are needed to correct deletion and/or insertion errors after codeword boundaries have been detected. The codebooks presented in this paper consist of codewords divided into segments. By imposing restrictions on the segments, the codewords are synchronizable. One deletion error can be detected and corrected per segment

Reducing the probability of sync-word false acquisition with Reed-Solomon codes

In our previous work we introduced a method for avoiding/excluding some symbols in Reed-Solomon (RS) codes, called symbol avoidance. In this paper, we apply the symbol avoidance method in sync-word based synchronization of RS encoded data. With the symbol avoidance method we reduce the probability of the RS encoded data being mistaken for the sync-word used to delimit the start/end of the data. The symbols in the RS code are avoided according to the sync-word used, such that the sync-word has very low probability of being found in the RS codewords, where it was not inserted. Therefore, for different sync-words, different symbols need to be avoided in the RS code. The goal here is to reduce the probability of false acquisition of the sync-word in the RS encoded framed data

Reducing the probability of sync-word false acquisition with Reed-Solomon codes

In our previous work we introduced a method for avoiding/excluding some symbols in Reed-Solomon (RS) codes, called symbol avoidance. In this paper, we apply the symbol avoidance method in sync-word based synchronization of RS encoded data. With the symbol avoidance method we reduce the probability of the RS encoded data being mistaken for the sync-word used to delimit the start/end of the data. The symbols in the RS code are avoided according to the sync-word used, such that the sync-word has very low probability of being found in the RS codewords, where it was not inserted. Therefore, for different sync-words, different symbols need to be avoided in the RS code. The goal here is to reduce the probability of false acquisition of the sync-word in the RS encoded framed data

Application of symbol avoidance in reed-solomon codes to improve their synchronization

Abstract: In our previous work we introduced a method for avoiding/excluding some symbols in Reed-Solomon (RS) codes, called symbol avoidance. In this paper, we apply the symbol avoidance method to make synchronization of RS encoded data more effective. We avoid symbols in a RS code and then perform conventional frame synchronization on RS encoded data by appending sync-words on the data. The symbols in the RS code are avoided according to the sync-word used, such that the sync-word has very low probability of being found in the RS codewords, where it was not inserted. Therefore, for different sync-words, different symbols need to be avoided in the RS code. The goal here is to reduce the probability of mistaking data for the sync-word in the RS encoded framed data. Hence, the probability of successful synchronization is improved. Not only does our symbol avoidance code improve probability of successful synchronization, it also reduces the overall amount of redundancy required when the channel is very noisy

Codes for protection from synchronization loss and additive errors

Codes for protection from synchronization loss and additive error

Comma-free Codes Over Finite Alphabets

Comma-free codes have been widely studied in the last sixty years, from points of view as diverse as biology, information theory and combinatorics. We develop new methods to study comma-free codes achieving the maximum size, given the cardinality of the alphabet and the length of the words. Specifically, we are interested in counting the number of such codes. We provide (two different proofs for) a closed-formula. The approach introduced is further developed to tackle well-known sub-families of comma-free codes, such as self-complementary and (generalisations of) non-overlapping codes. We also study codes that are not contained in strictly larger ones. For instance, we determine the maximal size of self-complementary comma-free codes and the number of codes reaching the bound. We provide a characterisation of-letter non-overlapping codes (over an alphabet of cardinality n), which allows us to devise the number of such codes that are not contained in any strictly larger one. Our approach mixes combinatorial and graph-theoretical arguments

Communication Systems Design for Downhole Acoustic Telemetry

The goal of this dissertation is to design a reliable and efficient communication system for downhole acoustic communication. This system is expected to operate in two different modes. A broadband high data rate mode in case of transmission of an image or a video file and a narrowband low data rate mode in case of transmission of sensor readings. This communication system functions by acoustic vibration of the pipes and uses them as the channel instead of installing long cables in areas that are hard to reach. However, this channel has unique characteristics where it exhibits several passbands and stopbands across the frequency spectrum. The communication system is expected to get around those challenges in both modes of operation. In the broadband case, the system uses Orthogonal Frequency Division Multiplexing to transmit data across multiple orthogonal frequencies spanning multiple passbands combined with an error-correction code to recover some of the losses caused by the channel. In the narrowband case, a short packet is transmitted at a low data rate where the signal spectrum can fit inside one passband. However, transmitting short packets induces a new synchronization problem. This dissertation investigates and explores in detail the problem of synchronization on short packets where each synchronization stage is examined. A simple algorithm that exploits the presence of error-correction codes is proposed for the frame synchronization stage and demonstrated to approach the optimal solution. Then, all synchronization stages are combined in order to study the effect of propagated errors caused by imperfect synchronization from one stage to the next and what can be done in the design of the packet and the receiver structure to mitigate those losses. The resulting synchronization procedure is applied to the pipe strings and demonstrated to achieve desirable levels of performance with the assistance of equalization at the receiver