Finite-precision analysis of demappers and decoders for LDPC-coded M-QAM systems

LDPC codes are state-of-art error correcting codes, included in several standards for broadcast transmissions. Iterative soft-decision decoding algorithms for LDPC codes reach excellent error correction capability; their performance, however, is strongly affected by finite-precision issues in the representation of inner variables. Great attention has been paid, in recent literature, to the topic of quantization for LDPC decoders, but mostly focusing on binary modulations and analysing finite precision effects in a disaggregrated manner, i.e., considering separately each block of the receiver. Modern telecommunication standards, instead, often adopt high order modulation schemes, e.g. M-QAM, with the aim to achieve large spectral efficiency. This puts additional quantization problems, that have been poorly debated in previous literature. This paper discusses the choice of suitable quantization characteristics for both the decoder messages and the received samples in LDPC-coded systems using M-QAM schemes. The analysis involves also the demapper block, that provides initial likelihood values for the decoder, by relating its quantization strategy with that of the decoder. A new demapper version, based on approximate expressions, is also presented, that introduces a slight deviation from the ideal case but yields a low complexity hardware implementation.