Since BICM-ID is a concatenation between channel coding and mapping, its performances strongly depend on the matching between mapping rule and code structure. In our previous papers, we proposed a yet very simple, close Shannon limit achieving BICM-ID system. It uses very simple codes, irregular repetition and single parity check codes, combined with extended mapping. Even though we know that the key role played towards the optimal design of the proposed code is the degree allocation for variable nodes, the irregular degree allocation to the node degrees were determined only empirically, by try-and error. This paper shows that the problem of the optimal degree allocation for the proposed BICM-ID technique can be solved by using linear programming technique. Results shows we can achieve better matching between the de-mapper and decoder curves, by which we can achieve even closer threshold to the Shannon limit and also lower error floor.

This article proposes a novel design framework, EXIT-constrained binary switching algorithm (EBSA), for achieving near Shannon limit performance with single parity check and irregular repetition coded bit interleaved coded modulation and iterative detection with extended mapping (SI-BICM-ID-EM). EBSA is composed of node degree allocation optimization using linear programming (LP) and labeling optimization based on adaptive binary switching algorithm jointly. This technique achieves exact matching between the Demapper (Dem) and decoder's extrinsic information transfer (EXIT) curves while the convergence tunnel opens until the desired mutual information (MI) point. Moreover, this article proposes a combined use of SI-BICM-ID-EM with Doped-ACCumulator (D-ACC) and modulation doping (MD) to further improve the performance. In fact, the use of D-ACC and SI-BICM-ID (noted as DSI-BICM-ID-EM) enables the right-most point of the EXIT curve of the combined demapper and D-ACC decoder (D dacc ), denoted as DemD dacc , to reach a point very close to the (1.0, 1.0) MI point. Furthermore, MD provides us with additional degree-of-freedom in "bending" the shape of the demapper EXIT curve by choosing the mixing ratio of modulation formats, and hence the left most point of the demapper EXIT curve can flexibly be lifted up/pushed down with MD aided DSI-BICM-ID-EM (referred to as MDSI-BICM-ID-EM). Results of the simulations show that near-Shannon limit performance can be achieved with the proposed technique; with a parameter set obtained by EBSA for MDSI-BICM-ID-EM, the threshold signal-to-noise power ratio (SNR) is only roughly 0.5 dB away from the Shannon limit, for which the required computational complexity per iteration is at the same order as a Turbo code with only memory-2 convolutional constituent codes.

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