On matching short LDPC codes with spectrally-efficient modulation

The combination of low-density parity-check (LDPC) codes and higher-order modulation does usually neither require an interleaver in between nor elaborated signal mapping design rules. However, as the constellation size increases, a matching interleaver can be employed to compensate performance losses, especially in case of structured codes. This interleaver can be generally described by mapping distributions. In this paper, we discuss optimized mapping distributions for short LDPC codes, i.e. in the order of 10²-10³ bits. We point out that mapping distributions optimized by means of density evolution may not be suited for short codes. An alternative framework is introduced that utilizes an extended version of extrinsic information transfer functions. Their visualization feature helps to identify good mapping distributions for short codes.