To alleviate the suboptimal performance of belief propagation (BP) decoding of short low-density parity-check (LDPC) codes, a plethora of improved decoding algorithms has been proposed over the last two decades. Many of these methods can be described using the same general framework, which we call ensemble decoding: A set of independent constituent decoders works in parallel on the received sequence, each proposing a codeword candidate. From this list, the maximum likelihood (ML) decision is designated as the decoder output. In this paper, we qualitatively and quantitatively compare different realizations of the ensemble decoder, namely multiple-bases belief propagation (MBBP), automorphism ensemble decoding (AED), scheduling ensemble decoding (SED), noise-aided ensemble decoding (NED) and saturated belief propagation (SBP). While all algorithms can provide gains over traditional BP decoding, ensemble methods that exploit the code structure, such as MBBP and AED, typically show greater performance improvements.

翻译：为改善短长度低密度奇偶校验（LDPC）码置信传播（BP）解码的次优性能，过去二十年间已涌现大量改进的解码算法。其中许多方法可采用统一的通用框架进行描述，我们称之为集成解码：一组独立的子解码器并行处理接收序列，各自生成候选码字。从该列表中，将最大似然（ML）判决指定为解码器输出。本文从定性与定量两个维度比较集成解码器的不同实现方案，包括多基置信传播（MBBP）、自同构集成解码（AED）、调度集成解码（SED）、噪声辅助集成解码（NED）以及饱和置信传播（SBP）。尽管所有算法均能较传统BP解码获得性能增益，但利用码结构的集成方法（如MBBP与AED）通常展现出更显著的性能提升。