The finite length analysis of spatially-coupled codes for 1-D magnetic recording channels

Spatially-coupled (SC) codes have recently attracted significant attention due to their capability to achieve capacity approaching performance. Significant recent research has been devoted to the asymptotic study of SC codes. Although the asymptotic analysis is relevant, it cannot be directly applied in the finite-length setting due to cycle-free and averaging assumptions. In this paper, we consider the problem of finite length analysis of SC codes for magnetic-recording (MR) applications. First, we propose an efficient approach to enumerate certain combinatorial objects inside the Tanner graph representation of SC codes, objects that are found to lead to decoding errors in the high reliability regime. This enumeration approach exploits the structure of SC codes to dramatically decrease the complexity of the enumeration. Next, we consider the class of array-based SC codes with column weight 3 as a representative example, and identify the problematic combinatorial objects that cause performance degradation in the error floor area. We show that SC codes designed to have a minimal number of these problematic objects have a notable performance improvement in the error floor area.