| Author: | Xue, Tianbo |
| Title: | Error correction codes for channels with insertion, deletion and substitution errors |
| Advisors: | Lau, C. M. Francis (EIE) |
| Degree: | M.Phil. |
| Year: | 2023 |
| Subject: | Error-correcting codes (Information theory) Hong Kong Polytechnic University -- Dissertations |
| Department: | Department of Electronic and Information Engineering |
| Pages: | xxii, 127 pages : color illustrations |
| Language: | English |
| Abstract: | Error correction codes play an important role in protecting the integrity and accuracy of data transmitted in digital communication systems and data kept in storage systems. Besides substitution errors caused by noise, insertion and deletion errors may occur. Insertion and deletion errors are also categorized as synchronization errors because they affect the synchronization of a communication channel. Some recent studies have focused on coding against insertions and deletions due to some specific practical communication and storage applications. Unlike error correction codes for substitution errors, codes for insertion and deletion errors are limited. The thesis is therefore devoted to the study of error correction codes for channels impaired by insertion, deletion and substitution errors. We first propose a new class of systematic comma-free code which can recover synchronization efficiently after insertion, deletion and substitution errors occur. The proposed code provides more choices in designing synchronization codes, and includes the classical F code as a special case. Then, we investigate codes that can correct insertion, deletion and substitution errors. We optimize the inner code of the classic Davey MacKay watermark code by proposing a soft-decision decoding based on a new metric and by enhancing the inner sparsified codebook based on better distance property and lowest-density property. We further propose a concatenated code composed of an RS outer code and a marker inner code. The proposed code not only is effective in correcting multiple insertion, deletion and substitution errors, but possesses a lower complexity decoding algorithm. Finally, we propose codes for practical systems. We propose a probabilistic channel model with correlated insertion and deletion errors, in addition to substitution errors. The channel model captures the data dependence adapted to applications such as the write channel in bit-patterned media recording systems. We also investigate the performance of a concatenated code, consisting of an outer low-density parity-check code and an inner marker code, over this channel. DNA-based data storage systems have become a hot research topic recently. Here, we propose a systematic error correction code that can combat insertion, deletion and substitution errors. By combining this code with a proposed modulation scheme, we construct GC-balanced DNA sequences with error correction capability. Throughout our investigations, computer simulations are used to evaluate the performance of the proposed error correction codes. Moreover, theoretical analyses are given whenever appropriate. |
| Rights: | All rights reserved |
| Access: | open access |
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