Finite-length scaling based on belief propagation for spatially coupled LDPC codes

TL;DR

This paper establishes a finite-length scaling law for spatially coupled LDPC codes by analyzing the equivalence of peeling decoding and belief propagation, simplifying complexity and improving understanding of decoding dynamics.

Contribution

It demonstrates the equivalence of peeling decoding and belief propagation for LDPC codes and derives a new scaling law for spatially coupled LDPC codes based on this insight.

Findings

Peeling decoding and belief propagation resolve the same variable nodes in each iteration.

Density evolution can be used to analyze the decrease of erased variable nodes.

A new finite-length scaling law for spatially coupled LDPC codes is established.

Abstract

The equivalence of peeling decoding (PD) and Belief Propagation (BP) for low-density parity-check (LDPC) codes over the binary erasure channel is analyzed. Modifying the scheduling for PD, it is shown that exactly the same variable nodes (VNs) are resolved in every iteration than with BP. The decrease of erased VNs during the decoding process is analyzed instead of resolvable equations. This quantity can also be derived with density evolution, resulting in a drastic decrease in complexity. Finally, a scaling law using this quantity is established for spatially coupled LDPC codes.