For low-density parity-check codes, spatial coupling was proved to boost the performance of iterative decoding up to the optimal performance. As an application of spatial coupling, in this paper, bit-interleaved coded modulation (BICM) with spatially coupled (SC) interleaving — called SC-BICM — is considered to improve the performance of iterative channel estimation and decoding for block-fading channels. In the iterative receiver, feedback from the soft-in soft-out decoder is utilized to refine the initial channel estimates in linear minimum mean-squared error (LMMSE) channel estimation. Density evolution in the infinite-code-length limit implies that the SC-BICM allows the receiver to attain accurate channel estimates even when the pilot overhead for training is negligibly small. Furthermore, numerical simulations show that the SC-BICM can provide a steeper reduction in bit error rate than conventional BICM, as well as a significant improvement in the so-called waterfall performance for high rate systems.

In this paper, we present a transmission scheme for a multiple-input multiple-output (MIMO) quasi-static fading channel with imperfect channel state information at the transmitter (CSIT). In this scheme, we develop a precoder structure to exploit the available CSIT and apply spatial coupling for further performance enhancement. We derive an analytical evaluation method based on extrinsic information transfer (EXIT) functions, which provides convenience for our precoder design. Furthermore, we observe an area property indicating that, for a spatially coupled system, the iterative receiver can perform error-free decoding even the original uncoupled system has multiple fixed points in its EXIT chart. This observation implies that spatial coupling is useful to alleviate the uncertainty in CSIT which causes difficulty in designing LDPC code based on the EXIT curve matching technique. Numerical results are presented, showing an excellent performance of the proposed scheme in MIMO fading channels with imperfect CSIT.

Kudekar et al. proved an interesting result in low-density parity-check (LDPC) convolutional codes: The belief-propagation (BP) threshold is boosted to the maximum-a-posteriori (MAP) threshold by spatial coupling. Furthermore, the authors showed that the BP threshold for code-division multiple-access (CDMA) systems is improved up to the optimal one via spatial coupling. In this letter, a phenomenological model for elucidating the essence of these phenomenon, called threshold improvement, is proposed. The main result implies that threshold improvement occurs for spatially-coupled general graphical models.

Kudekar et al. recently proved that for transmission over the binary erasure channel (BEC), spatial coupling of LDPC codes increases the BP threshold of the coupled ensemble to the MAP threshold of the underlying LDPC codes. One major drawback of the capacity-achieving spatially-coupled LDPC codes is that one needs to increase the column and row weight of parity-check matrices of the underlying LDPC codes. It is proved, that Hsu-Anastasopoulos (HA) codes and MacKay-Neal (MN) codes achieve the capacity of memoryless binary-input symmetric-output channels under MAP decoding with bounded column and row weight of the parity-check matrices. The HA codes and the MN codes are dual codes each other. The aim of this paper is to present an empirical evidence that spatially-coupled MN (resp. HA) codes with bounded column and row weight achieve the capacity of the BEC. To this end, we introduce a spatial coupling scheme of MN (resp. HA) codes. By density evolution analysis, we will show that the resulting spatially-coupled MN (resp. HA) codes have the BP threshold close to the Shannon limit.