Low-density parity-check (LDPC) codes are specified by graphs, and are the error correction technique of choice in many communications and data storage contexts. Message passing decoders diffuse information carried by parity bits into the payload, and this paper measures the value of engineering parity bits to be more reliable than message bits. We consider the binary symmetric channel (BSC) and measure the impact of unequal data protection on the threshold of a regular LDPC code. Our analysis also includes doping where the parity bits are known to the decoder. We investigate BSC with Gallager-A decoder, with a $3$-level-alphabet decoder, and with a full belief propagation decoder. We demonstrate through theoretical analysis and simulation that non-equiprobable inputs lead to significant improvements both in the threshold and in the speed with which the decoder converges. We also show that all these improvements are possible even with a simple $3$-level-alphabet decoder.

翻译：低密度奇偶校验（LDPC）码以图结构定义，是众多通信和数据存储场景中首选的纠错技术。消息传递解码器将校验比特携带的信息扩散至载荷中，本文评估了通过工程手段使校验比特比消息比特更可靠的价值。我们考虑二元对称信道（BSC），并测量非均衡数据保护对规则LDPC码阈值的影响。分析还包括解码器已知校验比特的掺杂情形。我们分别采用Gallagher-A解码器、三级字母表解码器以及全置信传播解码器对BSC进行研究。通过理论分析和仿真证明，非等概率输入在解码阈值和解码收敛速度上均能带来显著提升。我们还表明，即使使用简单的三级字母表解码器，所有这些改进也均可实现。