Efficient Probabilistic Design of High-Performance Modern Low-Density Parity-Check Codes

Date

2026-8-3

Author

Tanrıkulu, Ata Oğuz

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Because of their excellent asymptotic and finite-length (FL) performance, spatially-coupled (SC) codes are a class of low-density parity-check (LDPC) codes that has been gaining increasing attention. Multi-dimensional (MD) SC codes are constructed by connecting copies of an SC code via edge relocations. As the number of degrees of freedom in the SC and MD-SC code design increases, appropriately exploiting them becomes more difficult because of the resulting growth in complexity; hence, efficient FL algorithms are required to effectively exploit these degrees of freedom. In this thesis, we propose a novel probabilistic Markov chain Monte Carlo (MCMC) method to perform this FL optimization, addressing the removal of short cycles. While iterating, we draw samples from a defined distribution where the probability decreases as the number of short cycles from the previous iteration increases. We analyze our MCMC method theoretically as we prove the invariance of the Markov chain where each state represents a possible arrangement, i.e., sample, for the SC or MD-SC code design, which has a specific probability. Via our simulations, we then fit the distribution of the number of cycles resulting from a given arrangement on a Gaussian distribution. By analyzing the mean, we derive estimates for cycle counts that are close to the actual counts. We also propose a probabilistic framework to guide the MCMC algorithm for the MD-SC code design to obtain high-performance MD codes. In particular, we express the expected number of short cycles, which we seek to minimize, in the graph representation of the code in terms of the entries of a probability-distribution matrix that characterizes the MD-SC code design. We then find a locally-optimal probability distribution, which serves as the starting point of the MCMC algorithmic optimizer that produces the final MD-SC code. In addition to the theoretical analysis as well as the algorithms, we present experimental results demonstrating that, in orders of magnitude less overall time, our probabilistic frameworks produce codes with notably fewer short cycles and substantial gains in error/erasure-rate performance compared with the available state of the art.

Subject Keywords

LDPC Codes, MCMC Methods, Spatially-Coupled Codes, Multi-Dimentional Codes, Probabilistic Optimization

URI

https://hdl.handle.net/11511/120613

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Graduate School of Natural and Applied Sciences, Thesis