In this paper, overlapped circular spatially-coupled low-density parity-check codes (OC-LDPC) are proposed and their modified coupled codes are derived, which show better performance compared with the spatially-coupled low-density parity-check (SC-LDPC) codes. It is known that the SC-LDPC codes show asymptotically good performance when the chain length is sufficiently large. However, a large ch...

To my parents and my brother iii ACKNOWLEDGEMENTS I thank my advisor, Professor Steven W. McLaughlin for his guidance and constant encouragement that got me through every step in my PhD. He was very understanding and always rescued me whenever I got myself into trouble. It has been a pleasure and a privilege to work with him for the past five years. I would also like to take this opportunity to...

Abstract—In this paper, we present an error-trellis construction for tailbiting convolutional codes. A tailbiting error-trellis is characterized by the condition that the syndrome former starts and ends in the same state. We clarify the correspondence between code subtrellises in the tailbiting code-trellis and error subtrellises in the tailbiting error-trellis. Also, we present a construction ...

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In this paper, we investigate a code-dependent unequal power allocation method for Gaussian channels using irregular LDPC codes. This method allocates the power for each set of coded bits depending on the degree of their equivalent variable nodes. We propose a new algorithm to optimize the power allocation vector using density evolution algorithm under the Gaussian approximation. We show that u...

We present a symmetric LDPC code with constant rate and constant distance (i.e. good LDPC code) that its constraint space is generated by the orbit of one constant weight constraint under a group action. Our construction provides the first symmetric LDPC good codes. This solves the main open problem raised by Kaufman and Wigderson in [4].

This work explains the relationship between cycles, stopping sets, and dependent columns of the parity check matrix of low-density parity-check (LDPC) codes. Furthermore, it discusses how these structures limit LDPC code performance under belief propagation decoding. A new metric called extrinsic message degree (EMD) measures cycle connectivity in bipartite graphs. Using an easily computed esti...

Low Density Parity Check (LDPC) codes have attracted current researchers due to their excellent performance and capability of parallel decoding. One major criticism concerning LDPC codes has been their apparent high encoding complexity and memory inefficient nature due to large parity check matrix. This led the researchers to move into a memory efficient LDPC called Quasi-Cyclic (QC)-LDPC which...

The average bit erasure probability of a binary linear code ensemble under maximum a-posteriori probability (MAP) decoding over binary erasure channel (BEC) can be calculated with the average support weight distribution of the ensemble via the EXIT function and the shortened information function. In this paper, we formulate the relationship between the average bit erasure probability under MAP ...

Multi-Edge type Low-Density Parity-Check codes (METLDPC codes) introduced by Richardson and Urbanke are generalized LDPC codes which can be seen as LDPC codes obtained by concatenating several standard (ir)regular LDPC codes. We prove in this paper that MET-LDPC code ensembles possess a certain symmetry with respect to their Average Coset Weight Distributions (ACWD). Using this symmetry, we dri...