Quantum low-density parity check (LDPC) codes such as generalized toric codes with finite rate suggested by Tillich and Zémor offer an alternative route for quantum computation. Here, we study LDPC codes and show that any family of LDPC codes, quantum or classical, where distance scales as a positive power of the block length, has a finite error threshold. Based on that, we conclude that quantu...

In this paper, we review recent developments concerning the application of lowdensity parity-check (LDPC) codes to the Gilbert-Elliott (GE) channel. Firstly, we discuss the analysis of LDPC estimation-decoding in these channels using density evolution. We show that the required conditions of density evolution are satisfied in the GE channel, and that analysis demonstrates that large potential g...

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.

Low density parity check (LDPC) block codes have been shown to achieve near capacity performance for binary transmission over noisy channels. Block codes, however, require splitting the data to be transmitted into frames, which can be a disadvantage in some applications. Convolutional codes, on the other hand, have no such requirement, and are hence well suited for continuous transmission. In [...

Abstruct-Low Density Parity Check (LDPC) Codes provide near-Shannon Capacity performance for NASA Missions. These codes have high coding rates R=0.82 and 0.875 with moderate code lengths, n=4096 and 8176. Their decoders have inherently parallel structures which allows for high-speed implementation. Two codes based on Euclidean Geometry (EG) were selected for flight ASIC implementation. These co...

We investigate the application of low-density parity-check (LDPC) codes in volume holographic memory (VHM) systems. We show that a carefully designed irregular LDPC code has a very good performance in VHM systems. We optimize high-rate LDPC codes for the nonuniform error pattern in holographic memories to reduce the bit error rate extensively. The prior knowledge of noise distribution is used f...

It has been shown earlier and rediscovered recently that Low-Density Parity Check Codes can achieve bit error rate near to Shannon limit. They can be decoded using soft decision iterative decoding scheme. As low cost, high performance DSPs are widespread, DSP implementation for LDPC decoder is a viable option. Floating point implementation has higher costs and so fixed point DSP implementation ...

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...

We design low-density parity-check (LDPC) codes that perform at rates extremely close to the Shannon capacity. The codes are built from highly irregular bipartite graphs with carefully chosen degree patterns on both sides. Our theoretical analysis of the codes is based on [1]. Assuming that the underlying communication channel is symmetric, we prove that the probability densities at the message...

This paper presents the construction of large girth Quasi-Cyclic low density parity check (QC-LDPC) codes. The row groups are paired two times the row weight which has cut down hardware implementation cost and complexity as compared to the connection of individual columns and rows. The construction of newly obtained codes gives a class of efficiently encodable quasi-cyclic LDPC codes.