Message alignment for discrete LDPC decoders with quadrature amplitude modulation

Recent works describe the design of discrete decoders for low-density parity-check codes by application of mutual information maximizing clustering algorithms in discrete density evolution. In the resulting discrete message passing decoders only integers are exchanged and node operations become simple lookup operations. Earlier works only describe discrete decoders for binary modulation schemes. This paper presents a new technique called message alignment which enables to design discrete decoders for higher-order modulation schemes. First, we design a channel output quantizer for quadrature amplitude modulation with the Information Bottleneck method. The quantizer attempts to preserve the relevant information on the modulation symbols. Afterwards, we illustrate that the assignment of several bits to one modulation symbol does not allow straightforward decoder design with the available discrete density evolution technique. The proposed message alignment solves this problem. The resulting discrete decoder is compared with state-of-the-art decoders using bit error rate simulations.