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Low-density parity-check (LDPC) codes are specified by graphs, and are theerror correction technique of choice in many communications and data storagecontexts. Message passing decoders diffuse information carried by parity bitsinto the payload, and this paper measures the value of engineering parity bitsto 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 aregular LDPC code. Our analysis also includes doping where the parity bits areknown to the decoder. We investigate BSC with Gallager-A decoder, with a$3$-level-alphabet decoder, and with a full belief propagation decoder. Wedemonstrate through theoretical analysis and simulation that non-equiprobableinputs lead to significant improvements both in the threshold and in the speedwith which the decoder converges. We also show that all these improvements arepossible even with a simple $3$-level-alphabet decoder.

LDPC Decoders Prefer More Reliable Parity Bits: Unequal Data Protection Over BSC