Channel coding may be viewed as the best-informed and most potent component of cellular communication systems, which is used for correcting the transmission errors inflicted by noise, interference and fading. The powerful turbo code was selected to provide channel coding for Mobile Broad Band (MBB) data in the 3G UMTS and 4G LTE cellular systems. However, the 3GPP standardization group has recently debated whether it should be replaced by Low Density Parity Check (LDPC) or polar codes in New Radio (NR), ultimately reaching the decision to adopt the () code family for enhanced Mobile Broad Band (eMBB) data and polar codes for eMBB control. This paper summarises the factors that influenced this debate, with a particular focus on the Application Specific Integrated Circuit (ASIC) implementation of the decoders of these three codes. We show that the overall implementation complexity of turbo, LDPC and polar decoders depends on numerous other factors beyond their computational complexity. More specifically, we compare the throughput, error correction capability, flexibility, area efficiency and energy efficiency of ASIC implementations drawn from 110 papers and use the results for characterising the advantages and disadvantages of these three codes as well as for avoiding pitfalls and for providing design guidelines.

Sparse subspace clustering (SSC) relies on sparse regression for accurate neighbor identification. Inspired by recent progress in compressive sensing, this paper proposes a new sparse regression scheme for SSC via two-step reweighted $\ell _{1} $ -minimization, which also generalizes a two-step $\ell _{1} $ -minimization algorithm introduced by E. J. Candès et al. in [ The Annals of Statistics , vol. 42, no. 2, pp. 669–699, 2014] without incurring extra algorithmic complexity. To fully exploit the prior information offered by the computed sparse representation vector in the first step, our approach places a weight on each component of the regression vector, and solves a weighted LASSO in the second step. We propose a data weighting rule suitable for enhancing neighbor identification accuracy. Then, under the formulation of the dual problem of weighted LASSO, we study in depth the theoretical neighbor recovery rates of the proposed scheme. Specifically, an interesting connection between the locations of nonzeros of the optimal sparse solution to the weighted LASSO and the indexes of the active constraints of the dual problem is established. Afterwards, under the semi-random model, analytic probability lower/upper bounds for various neighbor recovery events are derived. Our analytic results confirm that, with the aid of data weighting and if the prior neighbor information is accurate enough, the proposed scheme with a higher probability can produce many correct neighbors and few incorrect neighbors as compared to the solution without data weighting. Computer simulations are provided to validate our analytic study and evidence the effectiveness of the proposed approach.

To strike a balance between energy efficiency and data quality control, this paper proposes a sensor censoring scheme for distributed sparse signal recovery via compressive-sensing-based wireless sensor networks. In the proposed approach, each sensor node employs a sparse sensing vector with known support for data compression, meanwhile enabling making local inference about the unknown support of the sparse signal vector of interest. This naturally leads to a ternary censoring protocol, whereby each sensor: 1) directly transmits the real-valued compressed data, if the sensing vector support is detected to be overlapped with the signal support; 2) sends a one-bit hard decision if empty support overlap is inferred; and 3) keeps silent if the measurement is judged to be uninformative. Our design then aims at minimizing the error probability that empty support overlap is decided but otherwise is true, subject to the constraints on a tolerable false-alarm probability that non-empty support overlap is decided but otherwise is true, and a target censoring rate. We derive a closed-form formula of the optimal censoring rule; a low complexity implementation using bi-section search is also developed. In addition, the average communication cost is analyzed. To aid global signal reconstruction under the proposed censoring framework, we propose a modified ℓ ₁ -minimization based algorithm, which exploits certain sparse nature of the hard decision vector received at the fusion center. Analytic performance guarantees, characterized in terms of the restricted isometry property, are also derived. Computer simulations are used to illustrate the performance of the proposed scheme.

Conventional sparse phase retrieval schemes can recover sparse signals from the magnitude of linear measurements only up to a global phase ambiguity. This work proposes a novel approach that instead utilizes the magnitude of affine measurements to achieve ambiguity-free signal reconstruction. The proposed method relies on two-stage approach that consists of support identification followed by the exact recovery of nonzero signal entries. In the noise-free case, perfect support identification using a simple counting rule is guaranteed subject to a mild condition on the signal sparsity, and subsequent exact recovery of the nonzero signal entries can be obtained in closed-form. The proposed approach is then extended to two noisy scenarios, namely, sparse noise (or outliers) and non-sparse bounded noise. For both cases, perfect support identification is still ensured under mild conditions on the noise model, namely, the support size for sparse outliers and the power of the bounded noise. Under perfect support identification, exact signal recovery can be achieved using a simple majority rule for the sparse noise scenario, and reconstruction up to a bounded error can be achieved using linear least-squares (LS) estimation for the non-sparse bounded noise scenario. The obtained analytic performance guarantee for the latter case also sheds light on the construction of the sensing matrix and bias vector. In fact, we show that a near optimal performance can be achieved with high probability by the random generation of the nonzero entries of the sparse sensing matrix and bias vector according to the uniform distribution over a circle. Computer simulations using both synthetic and real-world data sets are provided to demonstrate the effectiveness of the proposed scheme.