-Error correction provides reliable information free from errors. BCH codes are widely used to perform error correction. However, in order to improve the reliability of error correction BCH codes have been replaced by Low Density Parity Check (LDPC) codes. LDPC codes are special class of error correcting codes widely used in communication and memory systems, due to its Shannon limit approaching...

BURST CORRECTION CODING FROM LOW-DENSITY PARITY-CHECK CODES Wai Han Fong, PhD George Mason University, 2015 Dissertation Director: Dr. Shih-Chun Chang Dissertation Co-Director: Dr. Shu Lin This thesis explores techniques and theoretical bounds on efficiently encodable low-density parity-check (LDPC) codes for correcting single and multiple bursts of erasures and/or errors. The approach is to co...

Low-density parity-check (LDPC) coded orthogonal-frequency-division multiplexing (OFDM) is studied as an efficient coded modulation technique suitable for fiber-optics communication systems. We show that in long-haul fiber optics communications LDPC-coded OFDM increases spectral efficiency and requires simple equalization to deal with chromatic dispersion. LDPC-coded OFDM is also a promising po...

Low-density parity-check (LDPC) codes are known to be one of the best error-correction coding (ECC) schemes in terms correction performance. They have been utilized many advanced data communication standards for which codecs typically implemented custom integrated circuits (ICs). In this paper, we present a research work that shows LDPC scheme can also applied system characterized by highly lim...

We consider in this paper regular and nearly regular quasi-cyclic low-density paritycheck (LDPC) codes, derived from families of difference sets. The codes have girth at least 6, and sparse parity-check matrices. They are designed to perform well when iteratively decoded with the sum-product decoding algorithm and to allow low complexity encoding.

Low-Density Parity-Check convolutional codes (LDPCccs) are very interesting for practical error-correction coding in wireless transmission as they have excellent performance and at the same time they allow for variable block size with low complexity encoding and decoding. As for all LDPC codes that are decoded by the sub-optimal (but highly efficient) Sum Product Algorithm, the cycles in the co...

We consider Gallager’s soft-decoding (belief propagation) algorithm for decoding low-density parity-check (LDPC) codes, when applied to an arbitrary binary-input symmetric-output channel. By considering the expected values of the messages, we derive both lower and upper bounds on the performance of the algorithm. We also derive various properties of the decoding algorithm, such as a certain rob...

The role of low density parity check principles in the design of group codes for coded modulation is examined. In this context, the structure of linear codes over certain rings Zm and Gm is discussed, and LDPC codes over these ring structures are designed.

Source coding with correlated decoder side information is considered. We impose the practical constraint that the encoder be unaware of even the statistical dependencies between source and side information. Two classes of rate-adaptive distributed source codes, both based on Low-Density Parity-Check (LDPC) codes, are developed and their design is studied. Specific realizations are shown to be b...

Low Density Parity Check (LDPC) codes have enjoyed increasing interest during recent years. In general these are described in the terminology of sparse bipartite graphs containing no 4 -cycles, but an alternative way to deal with them are a particular class of incidence structures, namely partial linear spaces. This paper shows how to obtain a large class of partial linear spaces from inversive...