Tree-Based Construction of LDPC Codes Having Good Pseudocodeword Weights
<|reference_start|>Tree-Based Construction of LDPC Codes Having Good Pseudocodeword Weights: We present a tree-based construction of LDPC codes that have minimum pseudocodeword weight equal to or almost equal to the minimum distance, and perform well with iterative decoding. The construction involves enumerating a $d$-regular tree for a fixed number of layers and employing a connection algorithm based on permutations or mutually orthogonal Latin squares to close the tree. Methods are presented for degrees $d=p^s$ and $d = p^s+1$, for $p$ a prime. One class corresponds to the well-known finite-geometry and finite generalized quadrangle LDPC codes; the other codes presented are new. We also present some bounds on pseudocodeword weight for $p$-ary LDPC codes. Treating these codes as $p$-ary LDPC codes rather than binary LDPC codes improves their rates, minimum distances, and pseudocodeword weights, thereby giving a new importance to the finite geometry LDPC codes where $p > 2$.<|reference_end|>
@article{kelley2005tree-based,
    title={Tree-Based Construction of LDPC Codes Having Good Pseudocodeword Weights},
    author={Christine Kelley, Deepak Sridhara, and Joachim Rosenthal},
    journal={arXiv preprint arXiv:cs/0510009},
    year={2005},
    archivePrefix={arXiv},
    eprint={cs/0510009},
    primaryClass={cs.IT math.IT}
}