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A ternary message passing (TMP) decoding algorithm for low-densityparity-check codes is developed. All messages exchanged between variable andcheck nodes have a ternary alphabet, and the variable nodes exploit softinformation from the channel. A density evolution analysis is developed forunstructured and protograph-based ensembles. For unstructured ensembles thestability condition is derived. Optimized ensembles for TMP decoding showasymptotic gains of up to 0.6 dB with respect to ensembles optimized for binarymessage passing decoding. Finite length simulations of codes from TMP-optimizedensembles show gains of up to 0.5 dB under TMP compared to protograph-basedcodes designed for unquantized belief propagation decoding.

Protograph-Based LDPC Code Design for Ternary Message Passing Decoding