Analyzing finite-length protograph-based spatially coupled LDPC codes

Abstract

Abstract-Eligible for student paper award. The peeling decoding for spatially coupled low-density parity-check (SC-LDPC) codes is analyzed for a binary erasure channel. An analytical calculation of the mean evolution of degree-one check nodes of protograph-based SC-LDPC codes is given and an estimate for the covariance evolution of degree-one check nodes is proposed in the stable decoding phase where the decoding wave propagates along the chain of coupled codes. Both results are verified numerically. Protograph-based SC-LDPC codes turn out to have a more robust behavior than unstructured random SC-LDPC codes. Using the analytically calculated parameters, the finitelength scaling laws for these constructions are given and verified by numerical simulations.

A Scaling Law to Predict the Finite-Length Performance of Spatially-Coupled LDPC Codes

“…Further, simulation results suggest that the form of the proposed expression to predict the performance of the (l, r, L) ensemble also applies to protograph-based SC-LDPC code ensembles if some parameters are adjusted appropriately [18].…”

Finite-length performance of multi-edge protograph-based spatially coupled LDPC codes

“…This copy-and-permute operation is called lifting and avoids small girths which often harm iterative decoding. In the following, we review four relevant constructions: the standard (l, r, L) P construction [6], a spatially coupled RA (SC-RA) construction [7] and a spatially coupled TAR4JA (SC-TAR4JA) construction [3].…”

“…Standard (l, r, L) P Construction As in [6], we couple L protographs of regular (l, r) codes to create an SC-LDPC protograph: each variable node (VN) at position u is connected to the check nodes (CNs) at u, u + 1, . .…”

“…In [5], the authors propose a scaling law for the binary erasure channel (BEC) and a random SC-LDPC code ensemble. This analysis was extended in [6] to a class of protograph-based SC-LDPC code ensembles, where it was shown that the protograph-structure improves the finite-length properties of the SC-LDPC code ensemble compared to random SC-LDPC codes.…”

“…We extend the analysis of finite-length protograph-based SC-LDPC codes in [6] to structures based on multiple edges between nodes and puncturing patterns. For instance, our analysis applies to SC-LDPC codes based on accumulate-repeatby-4-jagged-accumulate (TAR4JA) structures analyzed in [3] or repeat-accumulate (RA) structures in [7].…”