The fifth-generation wireless technology is primarily designed to address a wide range of use cases mainly categorized into the enhanced mobile broadband, ultra-reliable and low-latency communication, and massive machine-type communication segments. To efficiently serve some other use cases whose requirements lie in-between these main use cases, the 3rd generation partnership project (3GPP), in Rel-17, introduce support for the reduced capability new radio (NR) devices known as RedCap with lower cost and complexity compared to legacy 5G devices. The considered complexity reduction techniques are associated with degraded link performance and coverage for the physical channels. Particularly, for the physical downlink control channel (PDCCH), which requires careful consideration, the reduction of the user equipments’ (UEs) complexity and the associated coverage loss can lead to an increase in the PDCCH blocking probability. This, in turn, can impact either the latency or the network capacity depending on the scenario. In this paper, we investigate the PDCCH blocking probability metric for RedCap devices. Specifically, we evaluate the performance of blocking probability in terms of various parameters including the number of users, size of downlink control information, size of control resource set, and the number of PDCCH candidates. Our results demonstrate that the PDCCH blocking probability increases by reducing the number of antenna branches, the number of PDCCH candidates, control resource set, and by increasing the number of scheduled UEs. We also show that the impact of reducing the DCI size is marginal on the PDCCH blocking probability. Finally, we discuss potential solutions and design guidelines for reducing the PDCCH blocking probability.

We use the received bit information rate (RBIR) to analyze the performance of multi-layer transmission when combined with hybrid automatic repeat request (HARQ). The different layers are obtained from ordinary Gray-coded M-QAM and used for transmitting log2(M) codewords in parallel, exploiting that the different bits in Gray-coded M-QAM have very different reliability. The performance is analyzed when different layers are decoded in parallel (independently) as well as when successive decoding is used. In addition, we study how the RBIR can be used to select a suitable layer for a retransmission to further improve the performance. Simulation results based on a Wi-Fi like physical layer show that a significant gain compared to the standard approach can be achieved by using basic multilayer transmission, and also that using successive decoding and carefully selecting what layer to use for retransmission can give further gains.

Braided convolutional codes (BCCs) are a class of spatially coupled turbo-like codes that can be described by a (2), (3)-regular compact graph. In this paper, we introduce a family of (dv, dc)-regular GLDPC codes with convolutional code constraints (CC-GLDPC codes), which form an extension of classical BCCs to arbitrary regular graphs. In order to characterize the performance in the waterfall and error floor regions, we perform an analysis of the density evolution thresholds as well as the finite-length ensemble weight enumerators and minimum distances of the ensembles. In particular, we consider various ensembles of overall rate R = 1/3 and R = 1/2 and study the trade-off between variable node degree and strength of the component codes. We also compare the results to corresponding classical LDPC codes with equal degrees and rates. It is observed that for the considered LDPC codes with variable node degree dv> 2, we can find a CC-GLDPC code with smaller dvthat offers similar or better performance in terms of BP and MAP thresholds at the expense of a negligible loss in the minimum distance.

Spatially coupled turbo-like codes (SC-TCs) have been shown to have excellent decoding thresholds due to the threshold saturation effect. Furthermore, even for moderate block lengths, the simulation results demonstrate a very good bit error rate performance in the waterfall region. In this paper, we discuss the effect of spatial coupling on the performance of TCs in the finite block-length regime. We investigate the effect of coupling on the error floor performance of SC-TCs by establishing conditions under which the spatial coupling either preserves or improves the minimum distance of TCs. This allows us to investigate the error floor performance of SC-TCs by performing a weight enumerator function analysis of the corresponding uncoupled ensembles. Our results demonstrate that the spatial coupling changes the design trade-off between the waterfall and error floor performance. Instead of optimizing the belief propagation (BP) threshold of uncoupled TCs, which in turn leads to a higher error floor, we can take advantage of the threshold saturation property of the SC-TCs. Choosing strong ensembles, characterized by good maximum-a-posteriori (MAP) thresholds and low error floors, the corresponding SC-TCs are then able to simultaneously approach capacity and achieve very low error floor.

In this paper, we perform a threshold analysis of braided convolutional codes on the additive white Gaussian noise (AWGN) channel. The decoding thresholds are estimated by Monte-Carlo density evolution techniques and compared with approximate thresholds from an erasure channel prediction. The results show that, with spatial coupling, the predicted thresholds are very accurate and quickly approach capacity if the coupling memory is increased. For uncoupled ensembles with random puncturing, the prediction can be improved with help of the AWGN threshold of the unpunctured ensemble.

We introduce a unified ensemble for turbo-like codes (TCs) that contains the four main classes of TCs: parallel concatenated codes, serially concatenated codes, hybrid concatenated codes, and braided convolutional codes. We show that for each of the original classes of TCs, it is possible to find an equivalent ensemble by proper selection of the design parameters in the unified ensemble. We also derive the density evolution (DE) equations for this ensemble over the binary erasure channel. The thresholds obtained from the DE indicate that the TC ensembles from the unified ensemble have similar asymptotic behavior to the original TC ensembles.

In this paper, we introduce the concept of spatially coupled turbo-like codes (SC-TCs) as the spatial coupling of a number of turbo-like code ensembles. In particular, we consider the spatial coupling of parallel concatenated codes, introduced by Berrou et al., and that of serially concatenated codes (SCCs), introduced by Benedetto et al. Furthermore, we propose two extensions of braided convolutional codes (BCCs), and a class of turbo-like codes which have an inherent spatially coupled structure, to higher coupling memories, and show that these yield improved belief propagation (BP) thresholds as compared with the original BCC ensemble. We derive the exact density evolution (DE) equations for SC-TCs and analyze their asymptotic behavior on the binary erasure channel. We also consider the construction of families of rate-compatible SC-TC ensembles. Our numerical results show that the threshold saturation of the BP decoding threshold to the maximum a posteriori threshold of the underlying uncoupled ensembles occurs for large enough coupling memory. The improvement of the BP threshold is especially significant for SCCs and BCCs, whose uncoupled ensembles suffer from a poor BP threshold. For a wide range of code rates, SC-TCs show close-to-capacity performance as the coupling memory increases. We further give a proof of threshold saturation for SC-TC ensembles with identical component encoders. In particular, we show that the DE of SC-TC ensembles with identical component encoders can be properly rewritten as a scalar recursion. This allows us to define potential functions and prove threshold saturation using the proof technique recently introduced by Yedla et al.

Braided convolutional codes (BCCs) are a class of spatially coupled turbo-like codes with a structure that is similar to product codes or generalized LDPC codes. We derive explicit input/output transfer functions of the component convolutional decoders for the binary erasure channel (BEC). These are then used to formulate exact density evolution equations for blockwise BCCs under belief propagation (BP) decoding with optimal component APP decoders. Thresholds are computed for the coupled and uncoupled case, which is equivalent to tailbiting. Due to the relatively high rate of the component codes a significant threshold improvement by spatial coupling can be observed.