Performance of LDPC Decoders with Missing Connections

TL;DR

This paper analyzes how LDPC decoders perform when some connections are missing, showing that decoding remains robust with smooth threshold degradation and identifying effects like stochastic facilitation.

Contribution

It provides theoretical validation and analysis of LDPC decoder performance under missing connections, including convergence proofs and threshold characterizations.

Findings

Decoding thresholds degrade smoothly with missing connections

Decoding remains robust despite missing wires

Stochastic facilitation observed in Gallager B decoders

Abstract

Due to process variation in nanoscale manufacturing, there may be permanently missing connections in information processing hardware. Due to timing errors in circuits, there may be missed messages in intra-chip communications, equivalent to transiently missing connections. In this work, we investigate the performance of message-passing LDPC decoders in the presence of missing connections. We prove concentration and convergence theorems that validate the use of density evolution performance analysis. Arbitrarily small error probability is not possible with missing connections, but we find suitably defined decoding thresholds for communication systems with binary erasure channels under peeling decoding, as well as binary symmetric channels under Gallager A and B decoding. We see that decoding is robust to missing wires, as decoding thresholds degrade smoothly. Moreover, there is a stochastic facilitation effect in Gallager B decoders with missing connections. We also compare the decoding sensitivity with respect to channel noise and missing wiring.