To meet the stringent high-throughput demands of enhanced mobile broadband (eMBB), low-density parity-check (LDPC) decoding is limited to few iterations. This constraint usually degrades error-correcting performance, rousing a critical need for puncturing towards algorithmic enhancements. However, existing puncturing methods lack modulation and rate compatibility, converging to local optima due to greedy search strategies. To this end, this paper proposes a modulation and rate compatible puncturing (MrcPunc) for 5G LDPC codes. It incorporates three key techniques: 1)a revised protograph-based extrinsic information transfer (PEXIT) analysisfor accurate performance prediction, 2)a progressive multi-path search (PMPS) algorithmto avoid local optima, and 3)a compatibility optimizationsupporting various modulations and code rates. The MrcPunc yields up to 0.6 dB gain over the 5G standard puncturing under few-iteration condition without extra decoding complexity. It is noted that MrcPunc guarantees robustness against both larger iteration counts and mismatched modulations, alongside reducing the average number of decoding iterations.

In coding theory, codes are usually designed with a certain level of randomness to facilitate analysis and accommodate different channel conditions. However, the resulting random code constructed can be suboptimal in practical implementations. Represented by a bipartite graph, the Batched Sparse Code (BATS Code) is a randomly constructed erasure code that utilizes network coding to achieve near-optimal performance in wireless multi-hop networks. In the performance analysis in the previous research, it is implicitly assumed that the coded batches in the BATS code are independent. This assumption holds only asymptotically when the number of input symbols is infinite, but it does not generally hold in a practical setting where the number of input symbols is finite, especially when the code is constructed randomly. We show that dependence among the batches significantly degrades the code’s performance. In order to control the batch dependence through graphical design, we propose constructing the BATS code in a structured manner. A hardware-friendly structured BATS code called the Cyclic-Shift BATS (CS-BATS) code is proposed, which constructs the code from a small base graph using light-weight cyclic-shift operations. We demonstrate that when the base graph is properly designed, a higher decoding rate and a smaller complexity can be achieved compared with the random BATS code.

Batched network codes (BNCs) are a low-complexity solution for communication through networks with packet loss. Although their belief propagation (BP) performance is proved to approach capacity in the asymptotic regime, there is no evidence indicating that their BP performance is equally good in the finite-length regime. In this paper, we propose a protograph-based construction for BNCs, referred to as protograph-based BNCs (P-BNCs), which significantly differs from existing BNCs in three aspects: 1) The vast majority of existing construction methods mainly focus on the degree distribution of check nodes (CNs), whereas P-BNCs not only specify the degree distributions of CNs and variable nodes (VNs) but also partially constrain the connectivity between CNs and VNs. 2) Traditional BNCs use a fixed degree distribution to generate all batches, making their performance highly sensitive to channel conditions, but P-BNCs achieve good performance under varying channel conditions due to their rate-compatible structures. 3) The construction of P-BNCs takes into account joint BP decoding with a sparse precode, whereas traditional constructions typically do not consider a precode, or assume the presence of a precode that can recover a certain fraction of erasures. Due to these three improvements, P-BNCs not only have higher achievable rates under varying channel conditions, but more importantly, their BP performance is significantly improved at practical lengths.

Batched sparse (BATS) codes were proposed as a reliable communication solution for networks with packet loss. In the finite-length regime, the error probability of BATS codes under belief propagation (BP) decoding has been studied in the literature and can be analyzed by recursive formulae. However, all existing analyses have not considered precoding or have treated the BATS code and the precode as two separate entities. In this paper, we analyze the word-wise error probability of finite-length BATS codes with a precode under joint decoding, including BP decoding and maximum-likelihood (ML) decoding. The joint BP decoder performs peeling decoding on a joint Tanner graph constructed from both the BATS and the precode Tanner graphs, and the joint ML decoder solves a single linear system with all linear constraints implied by the BATS code and the precode. We derive closed-form upper bounds on the error probability for both decoders. Specifically, low-density parity-check (LDPC) precodes are used for BP decoding, and any generic precode can be used for ML decoding. Even for BATS codes without a precode, the derived upper bound for BP decoding is more accurate than the approximate recursive formula, and easier to compute than the exact recursive formula. The accuracy of the two upper bounds has been verified by many simulation results. Based on the two upper bounds, we formulate an optimization problem to optimize the degree distribution of LDPC-precoded BATS codes, which improves BP performance, ML performance, or both. In our experiments, to transmit 128 packets over a line network with packet loss, the optimized LDPC-precoded BATS codes reduce the transmission overhead to less than 50% of that of standard BATS codes under comparable decoding complexity constraints.

In this paper, we study a class of staircase codes (SCCs), which is constructed by algebraic and single-parity-check component codes. These codes are referred to as mixed-component SCCs (MC-SCCs). We propose a low-complexity ternary message passing decoding algorithm for MC-SCCs, where error-and-erasure decoding plays a core role and soft reliability is reconstructed by hard decisions and channel log-likelihood ratios. We develop the density evolution analysis that is applicable to both binary and non-binary algebraic codes to optimize the decoder. By properly selecting mixed components, we can construct low-error-floor MC-SCCs with a smaller size of decoding window (proportional to component lengths) and a faster speed of convergence compared with the conventional SCCs. Moreover, we verify that for various requirements of overhead and decoding window size, MC-SCCs can outperform the conventional SCCs with both BCH components in terms of both error-rate performance and decoding complexity.

This paper presents a product coding scheme based on binary images of Reed-Solomon (RS) codes and single-parity-check (SPC) codes for high-speed communications. Utilizing the special selection of components, we propose hybrid soft- and hard-decision iterative decoding (ID) algorithms for these codes, during which many RS component decoders can be early terminated. The proposed hybrid ID only exchanges ternary messages between component decoders and early stops the RS component decoders satisfying a proposed stopping criterion, thus low hardware and computational complexities are guaranteed. The hybrid ID of RS-SPC product codes not only performs comparable to the soft-decision decoding of low-density parity-check (LDPC) codes and block turbo codes (BTCs), but also takes much lower computational complexity and smaller decoder data flow. We also propose semi-analytical methods to estimate the waterfall and error-floor performances of the proposed scheme, which yield relatively accurate estimated results. The simulation results and error-floor estimations indicate that some good RS-SPC product codes have very low error floors that satisfy the requirements of optical systems.

This paper presents a ternary message passing (TMP) decoding algorithm for product codes constructed from binary image Reed-Solomon (RS) codes and single-parity-check (SPC) codes. All exchanged messages among component decoders in TMP decoding take value from a ternary alphabet {–1, 0, +1}, which gives a potential for designing fast decoders. In particular, intersymbol interference (ISI) channels are considered due to their applications in many high-speed systems. Moreover, we propose the density evolution (DE) analysis for RS-SPC product codes over AWGN and ISI channels. The DE analyses and simulation results show RS-SPC product codes under TMP decoding performs well in various channels.

In this paper, we focus on how to further improve the performance of short block-length low-density parity-check (LDPC) codes, especially the short LDPC codes in 5th generation (5G) New Radio (NR) systems. We propose an enhanced adaptive belief propagation (ABP) decoding algorithm with the assistance of partial cyclic redundancy check (CRC) bits. Meanwhile, the error detection ability can still be guaranteed by the remaining CRC bits and adaptive decoder parameters. Moreover, the proposed partial CRC-aided ABP (CA-ABP) decoding can be combined with the conventional BP decoding to further improve the performance. Simulation results show that compared with the BP decoding our proposed decoding method achieves an improvement in the error-correction performance.

In this paper, we propose a modified adaptive belief propagation (ABP) algorithm, which is referred to as the random ABP (R-ABP) algorithm, for decoding short channel codes adopted in the fifth generation (5G) New Radio (NR) wireless systems. Based on the cyclic redundancy check (CRC) concatenation structure of 5G channel codes, we can take partial or even all CRC bits into iterative R-ABP decoding to improve the error correction performance, while the error detection capability can still be guaranteed by the remaining CRC bits and a proposed threshold-based acceptance criterion. We call this improved R-ABP decoding the threshold-and-CRC-aided R-ABP (TCA-R-ABP) decoding. The simulation results show that our proposed TCA-R-ABP algorithm outperforms the state-of-the-art decoding algorithms for many 5G low-density parity-check (LDPC) and polar codes. Moreover, the proposed TCA-R-ABP algorithm leads to a unified decoder for LDPC and polar codes, which has the potential to be a lower-complexity decoder over the combination of the belief propagation (BP) and CRC-aided successive cancellation list (CA-SCL) decoders.

This paper presents a generalized construction of RS-SPC product codes. A low-complexity joint-decoding scheme is proposed for these codes, in which a BP-based iterative decoding is performed based on the binary expansion of the whole parity-check matrix. Various powerful RS codes can be used as the component codes for RS-SPC product codes, which gives a good performance for local decoding (decode a single component codeword). The proposed BP-based iterative decoding is a global decoding, and it achieves an error-correcting capability compa-rable to codes of large blocklengths. This two-phase decoding scheme preserves the low decoding latency and complexity of the local decoding while achieves high reliability through the global decoding. The complexity of the proposed iterative decoding is discussed, and the simulation results show the proposed scheme offers a good trade-off between the complexity and the error performance.

A long-standing problem in marker-based facial motion capture is what are the optimal facial mocap marker layouts. Despite its wide range of potential applications, this problem has not yet been systematically explored to date. This paper describes an approach to compute optimized marker layouts for facial motion acquisition as optimization of characteristic control points from a set of high-resolution, ground-truth facial mesh sequences. Specifically, the thin-shell linear deformation model is imposed onto the example pose reconstruction process via optional hard constraints such as symmetry and multiresolution constraints. Through our experiments and comparisons, we validate the effectiveness, robustness, and accuracy of our approach. Besides guiding minimal yet effective placement of facial mocap markers, we also describe and demonstrate its two selected applications: marker-based facial mesh skinning and multiresolution facial performance capture.

ABSTRACT Content‐based human motion retrieval is important for animators with the development of motion editing and synthesis, which need to search similar motions in large databases. Obtaining text‐based representation from quantization of mocap data turned out to be efficient. It becomes a fundamental step of many researches in human motion analysis. Geometric features are one of these techniques, which involve much prior knowledge and reduce data redundancy of numerical data. We describe geometric features as basic unit to define human motions (also called mo‐words) and view a human motion as a generative process. Therefore, we obtain topic motions, which possess more semantic information using latent Dirichlet allocation by learning from massive training examples in order to understand motions better. We combine probabilistic model with human motion retrieval and come up with a new representation of human motions and a new retrieval framework. Our experiments demonstrate its advantages, both for understanding motions and retrieval. Copyright © 2011 John Wiley & Sons, Ltd.