Our research is focused on mapping binary sequences to permutation sequences. It is established that an upper bound on the sum of the Hamming distance for all mappings exists, and this sum is used as a criterion to ascertain how good previously known mappings are. We further make use of permutation trellis codes to investigate the performance of certain permutation mappings in a power-line communications system, where background noise, narrow band noise and wide band noise are present. A new multilevel construction is presented next that maps binary sequences to permutation sequences, creating new mappings for which the sum of Hamming distances are greater than previous known mappings. It also proved that for certain lengths of sequences, the new construction can attain our new upper bound on the sum of Hamming distances. We further extend the multilevel construction by showing how it can be applied to other mappings, such as permutations with repeating symbols and mappings with nonbinary inputs. We also show that a subset of the new construction yields permutation sequences that are able to correct insertion and deletion errors as well. Finally, we show that long binary sequences, formed by concatenating the columns of binary permutation matrices, are subsets of the Levenshtein insertion/deletion correcting codes. / Prof. H. C. Ferreira

Detecting and correcting errors occurring in the transmitted data through a channel is a task of great importance in digital communication. In Error Correction Coding (ECC), some redundant data is added with the original data while transmitting. By exploiting the properties of the redundant data, the errors occurring in the data from the transmission can be detected and corrected. In this thesis, a new coding algorithm named Signal Point Target Code has been studied and various properties of the proposed code have been extended. Signal Point Target Code (SPTC) uses a predefined shape within a given signal constellation to generate a parity symbol. In this thesis, the relation between the employed shape and the performance of the proposed code have been studied and an extension of the SPTC are presented. This research presents simulation results to compare the performances of the proposed codes. The results have been simulated using different programming languages, and a comparison between those programming languages is provided. The performance of the codes are analyzed and possible future research areas have been indicated.

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International Telemetering Conference Proceedings / October 27-30, 1997 / Riviera Hotel and Convention Center, Las Vegas, Nevada / Sandia National Laboratories (SNL) currently achieves a bandwidth efficiency (h ) of 0.5 to 1.0 bps/Hz by using traditional modulation schemes, such as, BPSK and QFSK. SNL has an interest in increasing the present bandwidth efficiency by a factor of 4 or higher with the same allocated bandwidth (about 10 MHz). Simulations have shown that 32- QAM trellis-coded modulation (TCM) gives a good bit error rate (BER) performance, and meets the requirements as far as the bandwidth efficiency is concerned. Critical to achieving this is that the receiver be able to achieve timing synchronization. This paper examines a particular timing recovery algorithm for all-digital receivers. Timing synchronization in a digital receiver can be achieved in different ways. One way of achieving this is by interpolating the original sampled sequence to produce another sampled sequence synchronized to the symbol rate or a multiple of the symbol rate. An adaptive sampling conversion algorithm which performs this function was developed by Floyd Gardner in 1993. In the present work, his algorithm was applied to two different modulation schemes, BPSK and 4-ary PAM. The two schemes were simulated in the presence of AWGN and ISI along with Gardner’s algorithm for timing recovery, and a fractionally spaced equalizer (T/2 FSE) for equalization. Simulations show that the algorithm gives good BER performance for BPSK in all the situations, and at different sampling frequencies, but unfortunately poor performance for the 4-ary PAM scheme. This indicates that Gardner’s algorithm for sampling conversion is not suitable for multi-level signaling schemes.

Channel coding has been largely used for the purpose of improving error performance on a communications system. Typical methods based on added redundancy allow for error detection and correction, this improvement however comes at a cost of bandwidth. This thesis focuses on channel coding for the bandwidth-limited channel where no bandwidth expansion is allowed. We first discuss the idea of coding for the bandwidth-limited channel as seen from the signal space point of view where the purpose of coding is to maximize the Euclidian distance between constellation points without increasing the total signal power and under the condition that no extra bits can be added. We then see the problem from another angle and identify the tradeoffs related to bandwidth and error performance. This thesis intends to find a simple way of achieving an improvement in error performance for the bandwidth-limited channel without the use of lattice codes or trellis-coded modulation. The proposed system is based on convolutional coding followed by multilevel transmission. It achieved a coding gain of 2 dB on Eb/No or equivalently, a coding gain of approximately 2.7 dB on SNRnorm without increase in bandwidth. This coding gain is better than that obtained by a more sophisticated lattice code Gosset E8 at the same error rate.