This paper presents a new class of spatially coupled turbo-like codes (SC-TCs), namely half spatially coupled braided convolutional codes (HSC-BCCs) and half spatially coupled parallel concatenated codes (HSC-PCCs). Different from the conventional SC-TCs, the proposed codes have simpler and deterministic coupling structures. Most notably, the coupling of HSC-BCCs is performed by re-encoding the whole coupling sequence in the component encoder of one time instant, rather than spreading the coupling bits to component encoders of multiple time instants. This simplification not only addresses the window decoding threshold loss issue in existing BCCs, but also allows the proposed codes to attain very close-to-capacity performance with a coupling memory as small as 2. Both theoretical and numerical results are provided to demonstrate the performance advantages of the proposed codes over existing spatially coupled codes.

The optical communication system using pulse position modulation (PPM) and superconducting nanowire single-photon detectors (SNSPDs) has attracted considerable attention for deep space applications as it enables high speed data transmission at extremely low average signal power. The deadtime of SNSPD is a critical factor in such systems because it primarily affects the signal detection efficiency. This becomes even more crucial in high-speed systems, where the deadtime can span several symbol periods. We employ the Markov chain model to characterize the high-speed PPM-SNSPD system and investigate its behavior. Analytical expressions for symbol transition probabilities are derived to characterize system-level metrics, including the symbol error rate and achievable code rate. Analysis shows that deadtime introduces memory to the PPM-SNSPD channel, resulting in channel asymmetry. Through experimental verification and simulations, we confirmed the effectiveness of our analysis. In addition, a set of new log-likelihood ratio (LLR) expressions is proposed based on the new model. Compared with the commonly used Poisson LLR expression, our proposed LLR expressions show more than 0.5 dB performance gain.

A new class of spatially-coupled turbo-like codes (SC-TCs), dubbed generalized spatially coupled parallel concatenated codes (GSC-PCCs), is introduced. These codes are constructed by applying spatial coupling on parallel concatenated codes (PCCs) with a fraction of information bits repeated$q$times. GSC-PCCs can be seen as a generalization of the original spatially-coupled parallel concatenated codes proposed by Moloudiet al., 2017. To characterize the asymptotic performance of GSC-PCCs, we derive the corresponding density evolution equations and compute their decoding thresholds. The threshold saturation effect is observed and proven. Most importantly, we rigorously prove that the rate-$R$GSC-PCC ensemble with 2-state convolutional component codes achieves at least a fraction$1-\frac {R}{R+q}$of the capacity of the binary erasure channel (BEC) for repetition factor$q\geq 2$and this multiplicative gap vanishes as$q$tends to infinity. To the best of our knowledge, this is the first class of SC-TCs that are proven to be capacity-achieving. Further, the connection between the strength of the component codes, the decoding thresholds of GSC-PCCs, and the repetition factor is established. The superiority of the proposed codes with finite blocklength is exemplified by comparing their error performance with that of existing SC-TCs via computer simulations.

We introduce generalized spatially coupled parallel concatenated codes (GSC-PCCs), a class of spatially coupled turbo-like codes obtained by coupling parallel concatenated codes (PCCs) with a fraction of information bits repeated before the PCC encoding. GSC-PCCs can be seen as a generalization of the original spatially coupled parallel concatenated convolutional codes (SC-PCCs) proposed by Moloudi et al. [1]. To characterize the asymptotic performance of GSC-PCCs, we derive the corresponding density evolution equations and compute their decoding thresholds. We show that the proposed codes have some nice properties such as threshold saturation and that their decoding thresholds improve with the repetition factor$q$. Most notably, our analysis suggests that the proposed codes asymptotically approach the capacity as$q$tends to infinity with any given constituent convolutional code.

In this paper, we study a class of spatially coupled turbo codes, namely partially information- and partially parity-coupled turbo codes. This class of codes enjoy several advantages such as flexible code rate adjustment by varying the coupling ratio and the encoding and decoding architectures of the underlying component codes can remain unchanged. For this work, we first provide the construction methods for partially coupled turbo codes with coupling memory m and study the corresponding graph models. We then derive the density evolution equations for the corresponding ensembles on the binary erasure channel to precisely compute their iterative decoding thresholds. Rate-compatible designs and their decoding thresholds are also provided, where the coupling and puncturing ratios are jointly optimized to achieve the largest decoding threshold for a given target code rate. Our results show that for a wide range of code rates, the proposed codes attain close-to-capacity performance and the decoding performance improves with increasing the coupling memory. In particular, the proposed partially parity-coupled turbo codes have thresholds within 0.0002 of the BEC capacity for rates ranging from 1/3 to 9/10, yielding an attractive way for constructing rate-compatible capacity-approaching channel codes.

In this paper, we propose partially information coupled bit-interleaved polar coded modulation (PIC-BIPCM), which is a class of spatially coupled polar coding schemes designed for$2^{Q}$-ary modulations. Specifically, we consider PIC-BIPCM schemes respectively constructed with three BIPCM schemes: direct BIPCM, punctured BIPCM, and multi-kernel BIPCM. We analyze the error performance of the proposed PIC-BIPCM over the binary erasure channel (BEC) via density evolution. With the analysis as a guideline, we jointly design the positions of coupled bits and the modulation bit-mapper by taking into account the partial polarization of finite length polar codes as well as the unequal error protection of high order modulations. Simulation results demonstrate significant performance improvement of the proposed PIC-BIPCM over the uncoupled BIPCM on both BEC and AWGN channels.

Partially information coupled turbo codes (PICTCs) is a class of spatially coupled turbo codes that can approach the BEC capacity while keeping the encoding and decoding architectures of the underlying component codes unchanged. However, PIC-TCs have significant rate loss compared to its component rate-1/3turbo code, and the rate loss increases with the coupling ratio. To absorb the rate loss, in this paper, we propose the partially information coupled duo-binary turbo codes (PIC-dTCs). Given a rate-1/3 turbo code as the benchmark, we construct a duo-binary turbo code by introducing one extra input to the benchmark code. Then, parts of the information sequence from the original input are coupled to the extra input of the succeeding code blocks. By looking into the graph model of PICdTC ensembles, we derive the exact density evolution equations of the PIC-dTC ensembles, and compute their belief propagation decoding thresholds on the binary erasure channel. Simulation results verify the correctness of our theoretical analysis, and also show significant error performance improvement over the uncoupled rate-1/3 turbo codes and existing designs of spatially coupled turbo codes.

In this paper, we investigate the performance of a class of spatially coupled codes, namely partially information coupled turbo codes (PIC-TCs) over the binary erasure channel (BEC). This class of codes enjoy flexible code rate adjustment by varying the coupling ratio. Moreover, the coupling method can be directly applied to any component codes without changing the encoding and decoding architectures of the underlying component codes. However, the theoretical performance of PIC-TCs has not been fully investigated. For this work, we consider the codes that have coupling memory m and study the corresponding graph model. We then derive the exact density evolution equations for these code ensembles with any given coupling ratio and coupling memory m to precisely compute their belief propagation decoding thresholds for the BEC. Our simulation results verify the correctness of our theoretical analysis and also show better error performance over uncoupled turbo codes with a variety of code rates on the BEC.

We investigate the spatial coupling technique for coded modulation schemes. In particular, we design partially information coupled bit-interleaved polar coded modulation (PIC-BIPCM) schemes for Gray-labelled 16-ary quadrature-amplitude modulation (16-QAM) over AWGN channels. In order to improve the error performance of the BIPCM, we propose a method to appropriately choose the coupled information bits between consecutive polar code blocks (CBs). We also derive a closed form expression for the CB error rate of the designed PIC-BIPCM. Simulation results show that the proposed PIC-BIPCM can achieve a considerable gain over the uncoupled counterparts for variable code rates.

We propose a new class of spatially coupled polar codes, namely information coupled (IC) polar codes, to improve the error performance of finite length polar codes. In the proposed IC-polar codes, every two consecutive polar code blocks (CBs) in a frame are coupled by sharing a few information bits. We optimize the indices of coupling information so that the less reliable information bits in each CB can obtain more reliable messages from the consecutive CBs during decoding. A decoding scheme is proposed for the IC-polar codes. Simulation results show that the proposed IC-polar codes achieve a considerable gain over the uncoupled counterparts for variable code rates with a slightly increased decoding complexity.

We propose a new class of information-coupled Turbo codes to improve the transport block (TB) error rate performance for LTE systems. Meanwhile, we keep the LTE hybrid automatic repeat request protocol and the Turbo decoder for each code block (CB) unchanged. In the proposed codes, every two consecutive CBs in a TB are coupled together by sharing a few common information bits. We propose a feed-forward and feed-back decoding scheme to decode the whole TB by exploiting the coupled information between CBs. Numerical results show that the proposed codes achieve a signal-to-noise-ratio (SNR) gain of 0.28 dB to 0.72 dB over LTE Turbo codes for the simulated code parameters at a TB error rate level of 10-2.

We propose a new class of partially information-coupled (PIC) turbo codes to improve the transport block (TB) error rate performance for long-term evolution (LTE) systems, while keeping the hybrid automatic repeat request protocol and the turbo decoder for each code block (CB) unchanged. In the proposed codes, every two consecutive CBs in a TB are coupled together by sharing partial information bits. This coding structure introduces irregular variable node degree distributions in the Tanner graph of the PIC-turbo codes. We propose a feedforward and feedback decoding scheme and a windowed decoding scheme to decode the whole TB by exploiting the coupled information between CBs. We calculate the extrinsic information transfer (EXIT) functions for the PIC-turbo codes by assuming that the coupled information are perfectly decoded. An SNR gain upper bound of the PIC-turbo codes over the LTE turbo codes for various coupling ratios is derived by the calculated EXIT charts. Numerical results show that the proposed codes achieve an SNR gain of 0.26-0.73 dB for various code parameters at a TB error rate level of 10-2, which complies with the derived SNR gain upper bound.