# Non-Uniformly Coupled LDPC Codes: Better Thresholds, Smaller Rate-loss, and Less Complexity

## TL;DR

This paper demonstrates that non-uniform spatial coupling in LDPC codes improves decoding thresholds, reduces rate loss, and accelerates convergence, enabling practical low-error-floor codes with near-capacity performance.

## Contribution

It introduces non-uniform coupling strategies for LDPC codes that optimize thresholds and convergence speed while maintaining low complexity and rate loss.

## Key findings

- Non-uniform coupling yields better thresholds.
- Faster decoding convergence with non-uniform coupling.
- Potential for near-capacity performance with slight smoothing increases.

## Abstract

We consider spatially coupled low-density parity-check codes with finite smoothing parameters. A finite smoothing parameter is important for designing practical codes that are decoded using low-complexity windowed decoders. By optimizing the amount of coupling between spatial positions, we show that we can construct codes with excellent thresholds and small rate loss, even with the lowest possible smoothing parameter and large variable node degrees, which are required for low error floors. We also establish that the decoding convergence speed is faster with non-uniformly coupled codes, which we verify by density evolution of windowed decoding with a finite number of iterations. We also show that by only slightly increasing the smoothing parameter, practical codes with potentially low error floors and thresholds close to capacity can be constructed. Finally, we give some indications on protograph designs.