Stability of Iterative Decoding of Multi-Edge Type Doubly-Generalized LDPC Codes Over the BEC

TL;DR

This paper derives a precise stability condition for iterative decoding of complex multi-edge type D-GLDPC codes over the BEC, using EXIT charts and spectral radius analysis.

Contribution

It introduces a necessary and sufficient stability criterion for multi-edge type D-GLDPC codes, linking spectral radius of a polynomial matrix to decoding stability.

Findings

Stability condition expressed via spectral radius.

Applicable to arbitrary linear block component codes.

Enhances understanding of decoding dynamics for complex code ensembles.

Abstract

Using the EXIT chart approach, a necessary and sufficient condition is developed for the local stability of iterative decoding of multi-edge type (MET) doubly-generalized low-density parity-check (D-GLDPC) code ensembles. In such code ensembles, the use of arbitrary linear block codes as component codes is combined with the further design of local Tanner graph connectivity through the use of multiple edge types. The stability condition for these code ensembles is shown to be succinctly described in terms of the value of the spectral radius of an appropriately defined polynomial matrix.