Protograph-Based Batched Network Codes

TL;DR

This paper introduces protograph-based batched network codes (P-BNCs), which improve finite-length belief propagation performance and adaptability to channel variations by jointly designing code structure and connectivity.

Contribution

The paper proposes a novel protograph-based construction for BNCs that specifies node degree distributions, connectivity, and incorporates joint BP decoding with a precode, enhancing finite-length performance.

Findings

P-BNCs achieve higher rates under varying channel conditions.

P-BNCs significantly improve BP decoding performance at practical lengths.

The construction method enhances robustness compared to traditional BNCs.

Abstract

Batched network codes (BNCs) are a low-complexity solution for communication through networks with packet loss. Although their belief propagation (BP) performance is proved to approach capacity in the asymptotic regime, there is no evidence indicating that their BP performance is equally good in the finite-length regime. In this paper, we propose a protograph-based construction for BNCs, referred to as protograph-based BNCs (P-BNCs), which significantly differs from existing BNCs in three aspects: 1) The vast majority of existing construction methods mainly focus on the degree distribution of check nodes (CNs), whereas P-BNCs not only specify the degree distributions of CNs and variable nodes (VNs) but also partially constrain the connectivity between CNs and VNs. 2) Traditional BNCs use a fixed degree distribution to generate all batches, making their performance highly sensitive to channel conditions, but P-BNCs achieve good performance under varying channel conditions due to their rate-compatible structures. 3) The construction of PBNCs takes into account joint BP decoding with a sparse precode, whereas traditional constructions typically do not consider a precode, or assume the presence of a precode that can recover a certain fraction of erasures. Thanks to these three improvements, P-BNCs not only have higher achievable rates under varying channel conditions, but more importantly, their BP performance is significantly improved at practical lengths.