A protograph-based low-density parity-check (LDPC) code design technique for bandwidth-efficient coded modulation with probabilistic shaping is presented. The approach jointly optimizes the LDPC code node degrees and the mapping of the coded bits to the bit-interleaved coded modulation (BICM) bit-channels. For BICM with uniform inputs and for BICM with probabilistic shaping, binary-input symmetric-output surrogate channels for the code design are used. The constructed codes for uniform inputs perform as good as the multi-edge type codes of Zhang and Kschischang (2013). For 8-ASK and 64-ASK with probabilistic shaping, codes of rates 2/3 and 5/6 with blocklength 64800 are designed, which operate within 0.63 and 0.69 dB of $\frac{1}{2}\,\log_2(1+\text{SNR})$ for a target frame error rate of $10^{-3}$ at spectral efficiencies of 1.38 and 4.25 bits/channel use, respectively.

Protograph-Based LDPC Code Design for Shaped Bit-Metric Decoding

A protograph-based low-density parity-check (LDPC) code design technique for bandwidth-efficient coded modulation is presented. The approach jointly optimizes the LDPC code node degrees and the mapping of the coded bits to the bit-interleaved coded modulation (BICM) bit-channels. For BICM with uniform input and for BICM with probabilistic shaping, binary-input symmetric-output surrogate channels for the code design are used. The constructed codes for uniform inputs perform as good as the multi-edge type codes of Zhang and Kschischang (2013). For 8-ASK and 64-ASK with probabilistic shaping, codes of rates 2/3 and 5/6 with blocklength 64800 are designed, which operate within 0.63dB and 0.69dB of continuous AWGN capacity for a target frame error rate of 1e-3 at spectral efficiencies of 1.38 and 4.25 bits/channel use, respectively.

As a typical example of bandwidth-efficient techniques, bit-interleaved coded modulation with iterative decoding (BICM-ID) provides desirable spectral efficiencies in various wireless communication scenarios. In this paper, we carry out a comprehensive investigation on tail-biting (TB) spatially coupled protograph (SC-P) low-density parity-check (LDPC) codes in BICM-ID systems. Specifically, we first develop a two-step design method to formulate a novel type of constellation mappers, referred to as labeling-bit-partial-match (LBPM) constellation mappers , for SC-P-based BICM-ID systems. The LBPM constellation mappers can be seamlessly combined with high-order modulations, such as $M$ -ary phase-shift keying (PSK) and $M$ -ary quadrature amplitude modulation (QAM). Furthermore, we conceive a new bit-level interleaving scheme, referred to as variable node matched mapping (VNMM) scheme , which can substantially exploit the structure feature of SC-P codes and the unequal protection-degree property of labeling bits to trigger the wave-like convergence for TB-SC-P codes. In addition, we propose a hierarchical extrinsic information transfer (EXIT) algorithm to predict the convergence performance (i.e., decoding thresholds) of the proposed SC-P-based BICM-ID systems. Theoretical analyses and simulation results illustrate that the LBPM-mapped SC-P-based BICM-ID systems are remarkably superior to the state-of-the-art mapped counterparts. Moreover, the proposed SC-P-based BICM-ID systems can achieve even better error performance with the aid of the VNMM scheme. As a consequence, the proposed LBPM constellation mappers and VNMM scheme make the SC-P-based BICM-ID systems a favorable choice for the future-generation wireless communication systems.

Analysis and Optimization of Tail-Biting Spatially Coupled Protograph LDPC Codes for BICM-ID Systems

As a spectral-efficiency technique for unequal error protection (UEP), hierarchical modulation (HM) bit-interleaved coded modulation (BICM) with iterative decoding (ID) has attracted interests in the wireless communication community. In this article, we conduct an investigation on spatially coupled (SC) protograph low-density parity-check (P-LDPC)-coded $M$ -ary quadrature amplitude modulation (QAM) HM-BICM-ID systems. We first develop an information-theoretic methodology to calculate $(\log _{2}M)/2$ types of constellation-constrained average mutual information (AMI), which can be used to characterize the performance limits of different layers in the HM-BICM systems. We further propose a two-stage design approach to construct a novel type of constellations, called as structural quadrant (SQ) constellations, and develop a quadrant-based harmonic mean analysis to evaluate the nonfeedback and iterative-feedback asymptotic performance of the proposed constellations. In addition, we conceive a performance-analysis tool, referred to as multistream-based extrinsic information transfer (MS-EXIT) algorithm, for predicting the decoding thresholds of all individual coded-bit streams in the proposed SC P-LDPC-coded HM-BICM-ID systems. Simulation results not only agree well with the theoretical analyses but also indicate that the proposed SC P-LDPC-coded HM-BICM-ID systems are remarkably superior to the state-of-the-art counterparts. Thereby, the proposed SC P-LDPC-coded HM-BICM-ID systems are competent to provide diverse Quality of Service (QoS) for future wireless applications, such as 6G-enabled Internet of Things (IoT).

/pdf/spatially-coupled-protograph-ldpc-coded-hierarchical-57y6cx780q.pdf

Spatially Coupled Protograph LDPC-Coded Hierarchical Modulated BICM-ID Systems: A Promising Transmission Technique for 6G-Enabled Internet of Things

In this paper, a novel differential chaotic bit-interleaved coded modulation (DC-BICM) system is proposed for band-limited transmission. This system combines protograph-based low density parity check codes with constellation-based $M$ -ary differential chaos shift keying (DCSK) modulation by one bitwise interleaving. Bit error rate simulation results show that the system has higher coding gain compared with the constellation-based $M$ -ary DCSK modulation system with the same spectral efficiency over multipath Rayleigh fading channels. At the same time, several simulations and P-EXIT analysis are used to analyze the performance of the proposed system. It is found that there is a lot of room for optimization of the system by comparing decoding thresholds and simulation results. Moreover, the system with only partial channel state information has better performance and lower complexity compared with the traditional bit-interleaved coded modulation (BICM) direct-sequence-spread-spectrum system. As a result, the DC-BICM system is a good candidate for band-limited transmission.

/pdf/a-differential-chaotic-bit-interleaved-coded-modulation-56uliq7y15.pdf

A Differential Chaotic Bit-Interleaved Coded Modulation System Over Multipath Rayleigh Channels

The protograph LDPC (P-LDPC) coded modulation is an efficient scheme using the variable degree matched mapping (VDMM) based on the protograph structure We propose a VDMM optimization strategy, as a crucial part for the P-LDPC coded modulation, by checking different permutation patterns between the variable nodes in protograph and the modulated bits Then, we develop a modified EXIT analysis for evaluating the thresholds for P-LDPC coded modulation For some specified P-LDPC codes and 16QAM constellations, the optimum patterns for VDMM can be obtained by a limited number of searches based on the modified EXIT analysis We find that for a certain labeling, the edge distributions of the protogragh structure should be taken into consideration, rather than using the water-filling strategy or BICM approach Decoding simulations, being consistent with the numerical analysis results, show that P-LDPC coded modulation with the optimum pattern noticeably outperforms that with the conventional water-filling pattern

Optimized variable degree matched mapping for protograph LDPC coded modulation with 16QAM

The invention discloses a cyclic redundancy check-assisted convolutional code decoding method Improved Chase decoding is applied to a cyclic redundancy check and convolutional code-cascaded coding/decoding scheme The decoding method mainly comprises the following steps of: first performing corresponding convolutional code decoding on a received sequence according to an ending way of convolutional code coding, and performing primary cyclic redundancy check to judge whether a code word output by the convolutional code decoding is valid or not by utilizing cyclic redundancy check data in coding information bits; if the cyclic redundancy check determines the code word is valid, stopping the decoding and taking the code word as decoding output; if the cyclic redundancy check determines the code word is invalid, decoding bit soft information output by the convolutional code decoding by using the improved Chase decoding, and performing cyclic redundancy check on the code words output by the improved Chase decoding one by one; if the cyclic redundancy check determines a certain code word is valid, stopping the improved Chase decoding and taking the code word as the decoding output; and if the cyclic redundancy check determines no valid code word is obtained by the improved Chase decoding, stopping the decoding and determining the decoding is failed

Cyclic redundancy check-assisted convolutional code decoding method

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Optimized variable degree matched mapping for protograph LDPC coded modulation with 16QAM

Cyclic redundancy check-assisted convolutional code decoding method