Characterization of Demapper EXIT Functions with BEC a priori Information with Applications to BICM-ID

This paper introduces a less is more approach to the modelling of iterative decoding for bit-interleaved coded modulation (BICM). It considers modelling the iterative exchange of soft a priori information between the demapper and decoder with a binary erasure channel model. This simplification, unlike the usual additive white Gaussian noise (AWGN) channel model, allows us to express the extrinsic information transfer (EXIT) chart curves for the demapper with polynomials whose order makes explicit the degrees of freedom available for design. The accuracy of our expressions simplifies the design process enabling us to compare in a more manageable manner the key performance parameters: the BER performance and the convergence threshold. This enabled us to find the pairing of memory-two recursive systematic convolutional (RSC) codes and mappers that achieve the earliest convergence threshold for a target BER floor at convergence: for 8-PSK semi-set partitioning (SSP) was optimal and converged at a signal-to-noise ratio (SNR)= 3.0 dB for a BER target of at least 10^-5; two new mappings were the optimal pairings for 16-QAM, where the L4b2 mapping converged at 2.9 dB for a BER floor ≤ 3.46 × 10^-4 and the H2b2 mapping converged at 3.1 dB for a BER floor ≤ 2.44 × 10^-5.