Finite-Length Construction of High Performance Spatially-Coupled Codes via Optimized Partitioning and Lifting

Spatially-coupled (SC) codes are a family of graph-based codes that have attracted significant attention thanks to their capacity approaching performance and low decoding latency. An SC code is constructed by partitioning an underlying block code into a number of components and coupling their copies together. In this paper, we first introduce a general approach for the enumeration of detrimental combinatorial objects in the graph of finite-length SC codes. Our approach is general in the sense that it effectively works for SC codes with various column weights and memories. Next, we present a two-stage framework for the construction of high-performance binary SC codes optimized for additive white Gaussian noise channel; we aim at minimizing the number of detrimental combinatorial objects in the error floor regime. In the first stage, we deploy a novel partitioning scheme, called the optimal overlap partitioning, to produce optimal partitioning corresponding to the smallest number of detrimental objects. In the second stage, we apply a new circulant power optimizer to further reduce the number of detrimental objects in the lifted graph. An SC code constructed by our new framework has nearly 5 orders of magnitudes error floor performance improvement compared to the uncoupled setting.