Spatially-Coupled MacKay-Neal Codes with No Bit Nodes of Degree Two Achieve the Capacity of BEC

TL;DR

This paper proves that spatially-coupled MacKay-Neal codes without degree-two variable nodes can achieve the capacity of the binary erasure channel, addressing error floor issues present in previous designs.

Contribution

It introduces a new class of SC-MN codes with no degree-two variable nodes and proves their capacity-achieving property on BEC.

Findings

SC-MN codes with no degree-two variable nodes achieve BEC capacity

Elimination of degree-two nodes reduces error floors

Theoretical proof of capacity achievement

Abstract

Obata et al. proved that spatially-coupled (SC) MacKay-Neal (MN) codes achieve the capacity of BEC. However, the SC-MN codes codes have many variable nodes of degree two and have higher error floors. In this paper, we prove that SC-MN codes with no variable nodes of degree two achieve the capacity of BEC.