Low-complexity detection and decoding for LDPC-coded data storage channels

Abstract

LDPC codes have shown an excellent performance over various channels for different code lengths and rates, and they are finding their way to become the dominant coding scheme for various applications. As an emerging channel coding technique, LDPC codes are widely considered for digital storage systems. In this thesis, LDPC codes based on finite geometries are selected due to their great performance and structure. We will present the details of the construction and features of these codes. In this thesis, we investigate various detection and decoding techniques that exhibit different performance and complexity trade-offs. The optimal or near optimal methods usually impose an enormous amount of computations, and therefore, they may not be suitable for practical applications. On the other hand, sub-optimal algorithms may suffer from performance degradation. Our main goal in this thesis is to design low-complexity decoders and detectors that have near optimal performance. We first start by introducing a new LDPC decoder, and later, we consider the detection problem. Particularly, we consider low-complexity detection and decoding for LDPC-coded data storage channels. We introduce a new algorithm for decoding LDPC codes that has a complexity close to low-complexity algorithms, while its performance approaches the performance of the belief propagation (BP) algorithm. The BP algorithm is a well-known method for decoding LDPC codes with a great performance, but it has a high complexity.