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）码由图定义，是众多通信和数据存储场景中首选的纠错技术。消息传递译码器将奇偶位携带的信息扩散至有效载荷中，本文衡量了将奇偶位设计为比消息位更可靠的工程价值。我们考虑二进制对称信道（BSC），并测量非均衡数据保护对正则LDPC码阈值的影响。我们的分析还包括了译码器已知奇偶位的掺杂场景。我们使用Gallager-A译码器、$3$级字母表译码器以及完整置信传播译码器对BSC进行研究。通过理论分析和仿真证明，非等概率输入在阈值和译码器收敛速度两方面均能带来显著提升。我们还表明，即使使用简单的$3$级字母表译码器，这些改进也是可行的。