EXIT-constrained BICM-ID design using extended mapping

Abstract

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.

Code Design for Iterative Decoding of Multilevel Codes

“…In Example 3 we show the design of MLCM-ID using the turbo code (one family of sparse graph codes). However the removal of the error floor is not the principal objective of this paper, and we refer to, e.g., [22] for the possible solution. Fig.…”

“…Following the partial proof in Theorem 2B, equation (22) can be modified to (35), via some mathematical manipulation, shown at the bottom of the page. For simplicity, we assume m = 3.…”

“…Based on equation (9), A (i) PM can be written in the form of (22), shown at the bottom of the previous page. The details of the proof are given in Appendix B.…”

BICM-ID-Based IDMA: Convergence and Rate Region Analyses

“…Originally, the idea of the SPC-IrR BICM-ID technique is proposed in [8], where extended mapping (EM) is used for modulation to increase the degrees-of-freedom for flexibly changing the demapper's EXIT curve; with EM, multiple labeling patterns are mapped to a single constellation point, and the shape of the demapper's EXIT curve changes according to the labeling pattern allocation. To achieve good matching between the demapper and decoder's EXIT curves while keeping the convergence tunnel open until a point near (1.0, 1.0) mutual information (MI) point in the EXIT chart, [8] also introduces doped accumulator (DACC) and modulation mixing (MM) techniques. The labeling patterns and the SPC-IrR code parameters are optimized in a systematic way by using the EXIT-constrained binary switching algorithm (EBSA).…”

Performance Analysis and System Design for Hierarchical Modulated BICM-ID

“…Note that it is also possible to optimize mappings for BICM-ID using EXIT-chart matching[21],[36]-[38]. However, as they do not have hierarchical frameworks, we only consider distance properties for mapping optimization in this paper.…”