UCLA

The volume of data continues to rapidly grow as information pours from various platforms. The huge amount of data needs to be transferred and stored with extremely high reliability. The error correcting codes (ECCs) are an integral part of modern-day communication, computation, and data storage systems in order to safeguard data against the adverse effects of noise and interference. The spatially-coupled (SC) codes are a class of graph-based ECCs that have recently emerged as an excellent choice for error correction in modern data storage and communication due to their outstanding performance, low decoding latency, and simple implementation.

An SC code is constructed by coupling several instances of a block code into a single coupled chain. In the asymptotic limit of large code lengths, SC codes enjoy capacity achieving performance. Due to simplifying assumptions and averaging effects, results from the asymptotic domain are not readily translatable to the practical, finite-length setting. Despite this chasm, finite-length analysis of SC codes is still largely unexplored. We tackle the problem of finite-length optimized design of SC codes in the context of various channel models.

First, we present a systematic framework with low computational complexity for designing finite-length SC codes with superior error floor performance. Next, we tailor our design method for various channel models by targeting the combinatorial objects in the graph of SC codes that are detrimental over these settings. Then, we generalize our framework for the finite-length analysis and design of irregular SC codes. Finally, we increase the coupling dimensionality, and we present a novel systematic framework to efficiently connect several SC codes and construct multi-dimensional spatially-coupled (MD-SC) codes.

In this research, we use advanced mathematical techniques from algebra, combinatorics, graph theory, probability theory, and optimization theory to develop algorithms and design frameworks with affordable complexity. Our frameworks are especially beneficial for modern storage applications, e.g. magnetic-recording and Flash memories.