On the Mapping of Low-Density Parity-Check Codes for Bit-Interleaved Coded Modulation

Low-density parity-check (LDPC) codes are very powerful error correction codes for bit-interleaved coded modulation (BICM) schemes. In BICM schemes the bits of one symbol have unequal error protection. In this paper, we show how to improve the performance of given LDPC codes by mapping the variable nodes of certain degree in a special way to the different bit levels. Since the equivalent binary-input component channels for each individual bit level are not symmetric, we use the tool of i.i.d. channel adapters to force symmetry. After that, we optimize the mapping of the LDPC code to the different bit levels by a downhill algorithm that uses a generalized discretized density evolution to calculate the thresholds. We show by thresholds and by simulations that a special mapping of LDPC codes lowers the bit error rates compared to a random mapping of LDPC codes.