Doubly-Generalized LDPC Codes: Stability Bound over the BEC

Abstract

The iterative decoding threshold of low-density parity-check (LDPC) codes over the binary erasure channel (BEC) fulfills an upper bound depending only on the variable and check nodes with minimum distance 2. This bound is a consequence of the stability condition, and is here referred to as stability bound. In this paper, a stability bound over the BEC is developed for doubly-generalized LDPC codes, where the variable and the check nodes can be generic linear block codes, assuming maximum a posteriori erasure correction at each node. It is proved that in this generalized context as well the bound depends only on the variable and check component codes with minimum distance 2. A condition is also developed, namely the derivative matching condition, under which the bound is achieved with equality.

Submitted to IEEE Trans. on Inform. Theory

Cited by in corpus (7)

• Coded Slotted ALOHA: A Graph-Based Method for Uncoordinated Multiple Access
• High Throughput Random Access via Codes on Graphs: Coded Slotted ALOHA
• Spectral Shape of Doubly-Generalized LDPC Codes: Efficient and Exact Evaluation
• Growth Rate of the Weight Distribution of Doubly-Generalized LDPC Codes: General Case and Efficient Evaluation
• On a Class of Doubly-Generalized LDPC Codes with Single Parity-Check Variable Nodes
• On the Growth Rate of the Weight Distribution of Irregular Doubly-Generalized LDPC Codes
• Stability of Iterative Decoding of Multi-Edge Type Doubly-Generalized LDPC Codes Over the BEC