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Let $R$ be a principal ideal local ring of finite length with a finite residue field of odd characteristic. Denote by $G(R)$ the general linear group of degree two over $R$, and by $B(R)$ the Borel subgroup of $G(R)$ consisting of upper triangular matrices. In this article, we prove that the pair $(G(R), B(R))$ is a strong Gelfand pair. We also investigate the decomposition of the degenerate Gelfand-Graev (DGG) modules of $G(R)$. It is known that the non-degenerate Gelfand Graev module (also called non-degenerate Whittaker model) of $G(R)$ is multiplicity-free. We characterize the DGG-modules where the multiplicities are independent of the cardinality of the residue field. We provide a complete decomposition of all DGG modules of $G(R)$ for $R$ of length at most four., Comment: Preliminary version, 20 Pages

Riblets are a well-known passive drag reduction technique with the potential for as much as 9% reduction in the frictional drag force in laboratory settings, and proven benefits for large scale aircraft. However, less information is available on the applicability of these textures for smaller air/waterborne vehicles where assumptions such as periodicity and/or asymptotic nature of the boundary layer no longer apply and the shape of the bodies of these vehicles can give rise to moderate levels of pressure drag. Here, we explore the effect of riblets on both sides of a finite-size foil consisting of a streamlined leading edge and a flat body. We use high resolution two-dimensional, two-component particle image velocimetry, with a double illumination and consecutive-overlapping imaging technique to capture the velocity field in both the boundary layer and the far field. We find the local velocity profiles and shear stress distribution, as well as the frictional and pressure components of the drag force and show the possibility of achieving reduction in both the fictional and pressure components of the drag force and record cumulative drag reduction as much as 6%. We present the intertwined relationship between the distribution of the spanwise-averaged shear stress distribution, the characteristics of the velocity profiles, and the pressure distribution around the body, and how the local distribution of these parameters work together or against each other in enhancing or diminishing the drag-reducing ability of the riblets for the entirety of the body of interest.

In a classical wiretap channel setting, Alice communicates with Bob through a main communication channel, while her transmission also reaches an eavesdropper Eve through a wiretap channel. In this paper, we consider a general class of polar secrecy codes for wiretap channels and study their finite-length performance. In particular, bounds on the normalized mutual information security (MIS) leakage, a fundamental measure of secrecy in information-theoretic security frameworks, are presented for polar secrecy codes. The bounds are utilized to characterize the finite-length scaling behavior of polar secrecy codes, where scaling here refers to the non-asymptotic behavior of both the gap to the secrecy capacity as well as the MIS leakage. Furthermore, the bounds are shown to facilitate characterizing numerical bounds on the secrecy guarantees of polar secrecy codes in finite block lengths of practical relevance, where directly calculating the MIS leakage is in general infeasible.

The spectral properties of electrons confined in a wire-like quasi-one-dimensional (1D) elongated quantum dot (EQD) coupler between silicon qubits, are investigated with a newly developed valley-augmented unrestricted Hartree-Fock (va-UHF) method, generalized to include the valley degree of freedom treated as an isospin, allowing calculations for a large number of electrons. The lower energy symmetry-broken solutions of the self-consistent generalized Pople-Nesbet equations exhibit, for a confinement that has been modeled after an experimentally fabricated one in silicon, formation of Wigner-molecular polymeric (longitudinal) chains, initiating through charge accumulation at the edges of the finite-length quasi-1D wire. An increasing number of parallel zig-zag chains form as the number of electrons loaded into the confinement is increased, with the formation of newly added chains determined by the strength of the transverse harmonic confinement. The broken-symmetry va-UHF solutions, subsequently augmented by the quantum-mechanically required parity-restoration, go beyond the va-UHF single-determinant solution, predicting formation of entangled Wigner-molecular chains whose charge distributions obliterate the zig-zag organization of the broken-symmetry solutions. The symmetry-restored va-UHF methodology enables systematic investigations of multi-electron complex nano-scale confined structures that could be targeted for future imaging microscopy experiments in silicon and other materials (e.g., 1D domain walls in TMD materials), and quantum information utilization., Comment: 10 pages, 10 color figures. Accepted for publication in Physical Review Applied. For related papers, see https://sites.gatech.edu/cyannouleas/

Motivated by experiments employing ps-long, kilojoule laser pulses, we examined x-ray emission in a finite-length underdense plasma irradiated by such a pulse using two dimensional particle-in-cell simulations. We found that, in addition to the expected forward emission, the plasma also efficiently emits in the backward direction. Our simulations reveal that the backward emission occurs when the laser exits the plasma. The longitudinal plasma electric field generated by the laser at the density down-ramp turns around some of the laser-accelerated electrons and re-accelerates them in the backward direction. As the electrons collide with the laser, they emit hard x-rays. The energy conversion efficiency is comparable to that for the forward emission, but the effective source size is smaller. We show that the ps laser duration is required for achieving a spatial overlap between the laser and the backward energetic electrons. At peak laser intensity of $1.4\times 10^{20}~\rm{W/cm^2}$, backward emitted photons (energies above 100~keV and $10^{\circ}$ divergence angle) account for $2 \times 10^{-5}$ of the incident laser energy. This conversion efficiency is three times higher than that for similarly selected forward emitted photons. The source size of the backward photons ($5~\rm{\mu m}$) is three times smaller than the source size of the forward photons.

Majorana bound states (MBSs) located at the ends of a hybrid superconductor-semiconductor nanowire are only true zero modes if their characteristic localization length is much smaller than the nanowire length, $\xi_M\ll L$. Otherwise, their wave function overlap gives rise to a finite energy splitting that shows a characteristic oscillatory pattern $\sim e^{-2L/\xi_M}\cos(k_F L)$ versus external parameters that modify the Fermi momentum $k_F$. Detecting such "Majorana oscillations", measurable through low-bias conductance, has been proposed as a strategy for Majorana detection in pristine nanowires. Here we discuss how this detection scheme does not work in full-shell hybrid nanowires, an alternative design to partial-shell nanowires in which a superconductor shell fully wraps the semiconductor core. Using microscopic models, we provide both numerical simulations for Al/InAs hybrids as well as analytical approximations in terms of general nanowire parameters. We find that Majorana oscillations with flux in full-shell nanowires are absent in a wide portion of parameter space. This absence is not a signature of non-overlapping left- and right-end MBSs, but a consequence of the Majorana oscillation period being systematically larger than the flux window of odd Little-Parks lobes where Majorana zero-energy peaks are predicted to appear. Our results demonstrate that split near-zero modes or individual zero-energy crossings should not be dismissed as trivial even if they are found not to oscillate with flux., Comment: 15 pages, 9 figures. Final version

B. A. Barnes introduced so-called Fredholm elements in a semiprime ring whose definition is inspired by Atkinson's theorem. Here the socle of a semiprime ring generalizes the ideal of finite-rank operators on a Banach space. In this paper, we aim to see that the algebraic concept of the length of a module is strongly related to that of Fredholm elements. This motivates another generalization of Fredholm elements by requiring for an element $a\in\mathcal{A}$ that the $\mathcal{A}$-modules of the form $\mathcal{A}/\mathcal{A} a$ and $\mathcal{A}/a\mathcal{A}$ are of finite length. We are particularly interested in sufficient conditions for our generalized Fredholm elements to be Fredholm. In a unital C$^*$-algebra $\mathcal{A}$ we shall even see that an element $a\in\mathcal{A}$ is Fredholm if and only if the $\mathcal{A}$-modules $\mathcal{A}/\mathcal{A} a$ and $\mathcal{A}/a\mathcal{A}$ both have finite length.

A spin-wave theory that includes the antisymmetric Dzyaloshinskii-Moriya exchange interactions and long-range dipole-dipole interactions is presented for finite-length ferromagnetic spin chains. It is found that three different physical situations arise, depending on the direction chosen in this geometry for the axial vector of the Dzyaloshinskii-Moriya interactions. In some cases this leads to a tilting of the equilibrium orientations near the ends of the chain due to interfacial effects and with consequential effects on the spectrum of discrete dipole-exchange spin waves. When variations are introduced for the dominant bilinear exchange interactions at the ends of the spin chain, it is shown that localized spin waves with spatial decay characteristics may occur.

This paper investigates the relation between the second-order coding rate, where the second-order turns out to be strictly larger than $\sqrt{n}$, and the mutual information as the leaked information for a fixed error probability by using wiretap codes constructed by universal$_2$ hash functions. We first generalize the upper bound on $\epsilon$-smooth max information in \cite{tyagi} and use it in our analysis where we adopt the method in \cite{hayashi-tan}, which uses universal hashing for compressing a source and making it secure from another correlated source, and apply it to the wiretap channel. We prove first- and second-order achievability results by assuming that the conjecture we state holds true.

Bennett et al. proposed a family of protocols for entanglement distillation, namely, hashing, recurrence and breeding protocols. The last one is inferior to the hashing protocol in the asymptotic regime and has been investigated little. In this paper, we propose a framework of converting a stabilizer quantum error-correcting code to a breeding protocol, which is a generalization of the previous conversion methods by Luo-Devetak and Wilde. Then, show an example of a stabilizer that gives a breeding protocol better than hashing protocols, in which the finite number of maximally entangled pairs are distilled from the finite number of partially entangled pairs., Comment: 9 pages, latex2e, no figure, 1 table, v2 added the two important citations (see the acknowledgment)

The cloud radio access network (C-RAN) has become the foundational structure for various emerging communication paradigms, leveraging the flexible deployment of distributed access points (APs) and centralized task processing. In this paper, we propose a cross-layer optimization framework based on a practical finite-length coding communication system in C-RAN, aiming at maximizing bandwidth efficiency while providing statistical quality of service (QoS) for individual services. Based on the theoretical results from effective capacity and finite-length coding, we formulate a joint optimization problem involving modulation and coding schemes (MCS), retransmission count, initial bandwidth allocation and AP selection, which reflects the coordinated decision of parameters across the physical layer, data link layer and transport layer. To tackle such a mixed-integer nonlinear programming (MINLP) problem, we firstly decompose it into a transmission parameter decision (TPD) sub-problem and a user association (UA) sub-problem, which can be solved by a binary search-based algorithm and an auction-based algorithm respectively. Simulation results demonstrate that the proposed model can accurately capture the impact of QoS requirements and channel quality on the optimal transmission parameters. Furthermore, compared with fixed transmission parameter setting, the proposed algorithms achieve the bandwidth efficiency gain up to 27.87% under various traffic and channel scenarios., Comment: 13 pages, 17 figures

We introduce non-commutative algebras, which can be associated with the function algebra of functions on a finite or half-finite cylinder. The algebras, which depend on a deformation parameter, are crossed product algebras of a partial group action of $\mathbb{Z}$ on an interval of the real line $\mathbb{R}$. Discrete representations of the algebras can be seen as matrix regularizations of the respective function algebra on the finite or half-finite cylinder and therefore as fuzzy space. In a second part of the article, we review crossed product algebras based on partial group actions and derive the results needed in the first part., Comment: 40 pages

Finite-length armchair graphene nanoribbons can behave as one dimensional topological materials, that may show edge states in their zigzag-terminated edges, depending on their width and termination. We show here a full solution of Tight-Binding graphene rectangles of any length and width that can be seen as either finite-length armchair or zigzag ribbons. We find exact analytical expressions for both bulk and edge eigen-states and eigen-energies. We write down exact expressions for the Coulomb interactions among edge states and introduce a Hubbard-dimer model to analyse the emergence and features of different magnetic states at the edges, whose existence depends on the ribbon length. We find ample room for experimental testing of our predictions in N = 5 armchair ribbons. We compare the analytical results with ab initio simulations to benchmark the quality of the dimer model and to set its parameters. A further detailed analysis of the ab initio Hamiltonian allows us to identify those variations of the Tight-Binding parameters that affect the topological properties of the ribbons.

We construct moduli spaces of objects in an abelian categories satisfying some finiteness hypotheses. Our approach is based on the work of Artin-Zhang and the intrinsic construction of moduli spaces for stacks developed by Alper-Halpern-Leistner-Heinloth., Comment: 17 pages. Comments welcome

We consider two nonlinear equations, the Localized Induction Equation and the cubic nonlinear Schr\"odinger Equation, and prove that the solvability of certain initial-boundary value problems for each equation is equivalent through the generalized Hasimoto transformation. As an application, we prove the orbital stability of plane wave solutions of the nonlinear Schr\"odinger equation based on stability estimates obtained for the Localized Induction Equation by the author in a paper in preparation. As far as the author knows, this is the first time that the analysis of the Localized Induction Equation, along with the Hasimoto transformation, provided new insight for the nonlinear Schr\"odinger equation., Comment: 27 pages

Dense arrays can facilitate the integration of multiple antennas into finite volumes. In addition to the compact size, sub-wavelength spacing enables superdirectivity for endfire operation, a phenomenon that has been mainly studied for isotropic and infinitesimal radiators. In this work, we focus on linear dipoles of arbitrary yet finite length. Specifically, we first introduce an array model that accounts for the sinusoidal current distribution (SCD) on very thin dipoles. Based on the SCD, the loss resistance of each dipole antenna is precisely determined. Capitalizing on the derived model, we next investigate the maximum achievable rate under a fixed power constraint. The optimal design entails conjugate power matching along with maximizing the array gain. Our theoretical analysis is corroborated by the method of moments under the thin-wire approximation, as well as by full-wave simulations. Numerical results showcase that a super-gain is attainable with high radiation efficiency when the dipole antennas are not too short and thin., Comment: To appear in 2022 IEEE GLOBECOM

This study presents numerical simulations of the resonance of a finite-length granular chain of dissipative grains driven by a harmonically vibrated tube. Multiple gradual resonant modes, namely, non-resonance mode, partial-resonance mode, and complete-resonance mode, are identified. With a fixed vibration frequency, increased vibration acceleration leads to a one-by-one increase in the number of grains participating in resonance, which is equal to the number of grain-wall collisions in a vibration period. Compared with the characteristic time of the grain-grain and the grain-wall collisions, the time of free flight plays a dominant role in grain motion. This condition results in the occurrence of large opening gaps between the grains and independent grain-grain and gain-wall collisions. A general master equation that describes the dependence of the system energy on the length of the granular chain and the number of grain-wall collisions is established, and it is in good agreement with the simulation results. We observe a gradual step-jump increase in system energy when the vibration acceleration is continuously increased, which is dedicated to an individual energy injection. Moreover, two typical phase diagrams are discussed in the spaces of $\phi-\it{\Gamma}$ and $N-\it\Gamma$., Comment: 19 pages, 7 figures

Electrokinetic energy conversion provides a scheme for energy harvesting and storage for on-chip applications. However, the major drawback of electrokinetic energy conversion is its low conversion efficiency. Researchers are in a quest to find ways to improve this efficiency. With the same motive, we investigated the generation of streaming potential by applying surface modification and employing a non-Newtonian fluid to flow through the microchannel under constant pressure difference across its ends. Shear-thickening liquids tend to lessen electrokinetic effects, whereas shear-thinning liquids favour them. Also, having superhydrophobic surfaces improve the magnitude of generated streaming potential. We examine the combined effect of fluid rheology and surface modification on electrokinetic energy generation. We have learned intriguing insights about using non-Newtonian fluid in hydrophobic microchannels as an outcome of our combined research. Hydrophobic surfaces do not enhance the efficiency for a fluid with below a power law index of 0.7. The findings of this research can be used towards the selection of fluid-substrate combination that will optimize electrokinetic power generation efficiency.

We propose four finite-length scaling laws to predict the frame error rate (FER) performance of spatially-coupled low-density parity-check codes under full belief propagation (BP) decoding with a limit on the number of decoding iterations and a scaling law for sliding window decoding, also with limited iterations. The laws for full BP decoding provide a choice between accuracy and computational complexity; a good balance between them is achieved by the law that models the number of decoded bits after a certain number of BP iterations by a time-integrated Ornstein-Uhlenbeck process. This framework is developed further to model sliding window decoding as a race between the integrated Ornstein-Uhlenbeck process and an absorbing barrier that corresponds to the left boundary of the sliding window. The proposed scaling laws yield accurate FER predictions.

Part B (of a project involving four Parts) is about "bases of lines", a concept introduced by C. Herrmann and the author in the late 80's. Bases of lines attempt to describe a given modular lattice in a geometric way akin to how projective geometries describe complemented modular lattices. This e.g. yields the result that each modular lattice L of finite length d(L), and having s(L) many maximal congruences, has at least 2d(L)-s(L) many join-irreducible elements. Furthermore, an algorithm is proposed that calculates, in a compressed way, the (full) submodule lattice Sub(W) of any (sufficiently known) finite R-module W.

This is Part A of four Parts dedicated to modular lattices of finite length. It builds on 1992 notes of the author (available on ResearchGate), and in so doing heeds a wish of the late Gian-Carlo Rota. Part A is in fairly final form and mainly features known material, exceptions being a short proof of the distributivity of congruence lattices of lattices, as well as the concept of a point-splitting (which applies to arbitrary partial linear spaces). The planned content of Parts B,C,D is given in the introduction of Part A. Suffice it to say that deep results from C.Herrmann and R.Wille will be treated in English for the first time. All of this (even Part A) is work in process and comments/contributions are welcome., Comment: 38 pages, several figures with lattice diagrams

This study investigates the streaming instability triggered by ion motion in a plasma system that is finite in length, collisionless, and inhomogeneous. Employing numerical simulations using Particle-In-Cell (PIC) techniques and kinetic equations, the study examines how inhomogeneity emerges from integrating a cold ion beam with a background plasma within a confined system. The findings suggest that steady ion flow can modify ion sound waves through acoustic reflections from system boundaries, leading to instability. Such phenomena are known to be a hydrodynamic effect. However, there are also signatures of the beam-driven ion sound instability where kinetic resonances play a pivotal role. The main objective is to understand the impact of a finite-length system on beam-plasma instability and to identify the wave modes supported in such configurations., Comment: 21 pages, 11 figures

We construct a global Lindblad master equation for a Kitaev quantum wire of finite length, weakly coupled to an arbitrary number of thermal baths, within the Born-Markov and secular approximations. We find that the coupling of an external bath to more than one lattice site generates quantum interference effects, arising from the possibility of fermions to tunnel through multiple paths. In the presence of two baths at different temperatures and/or chemical potentials, the steady-state particle current can be expressed through the Landauer-B\"uttiker formula, as in a ballistic transport setup, with the addition of an anomaly factor associated with the presence of the $p$-wave pairing in the Kitaev Hamiltonian. Such a factor is affected by the ground-state properties of the chain, being related to the finite-size equivalent of its Pfaffian topological invariant., Comment: 14 pages, 9 figures. Final version

While analyzing the persistence length of DNA atomistic simulations Wu et al. [J. Chem. Phys. 142, 125103 (2015)] introduced an empirical formula to account for the observed length-dependence. In particular they found that the persistence length increases with the distance. Here, we derive the formula by Wu et al. using a non-local twistable wormlike chain which introduces couplings between distal sites. Finally, we show that the same formula can account for the length-scale dependence of the torsional persistence length and is, in fact, applicable to any kind of polymer model with non-local couplings., Comment: 3 pages, 1 Figure

We consider the usage of finite-length polar codes for the Gaussian multiple access channel (GMAC) with a finite number of users. Based on the interleave-division multipleaccess (IDMA) concept, we implement an iterative detection and decoding non-orthogonal multiple access (NOMA) receiver that benefits from a low complexity, while scaling (almost) linearly with the amount of active users. We further show the conceptual simplicity of the belief propagation (BP)-based decoder in a step-by-step illustration of its construction. Beyond its conceptual simplicity, this approach benefits from an improved performance when compared to some recent work tackling the same problem, namely the setup of finite-length forward errorcorrection (FEC) codes for finite-number of users. We consider the 5th generation mobile communication (5G) polar code with a block length $N = 512$ applied to both a two-user and a four-user GMAC scenario with a sum-rate of $R_{sum} = 0.5$ and $R_{sum} = 1$, respectively. Simulation results show that a BP-based soft interference cancellation (SoIC) receiver outperforms a joint successive cancellation (JSC) scheme. Finally, we investigate the effect of a concatenated repetition code which suggests that alternative polar code design rules are required in multi-user scenarios., Comment: Asilomar2020

We analyze the magnetic mode structure of axially-magnetized, finite-length, nanoscopic cylinders in a regime where the exchange interaction dominates, along with simulations of the mode frequencies of the ferrimagnet yttrium iron garnet. For the bulk modes we find that the frequencies can be represented by an expression given by Herring and Kittel by using wavevector components obtained by fitting the mode patterns emerging from these simulations. In addition to the axial, radial, and azimuthal modes that are present in an infinite cylinder, we find localized "cap modes" that are "trapped" at the top and bottom cylinder faces by the inhomogeneous dipole field emerging from the ends. Semi-quantitative explanations are given for some of the modes in terms of a one-dimensional Schrodinger equation which is valid in the exchange dominant case. The assignment of the azimuthal mode number is carefully discussed and the frequency splitting of a few pairs of nearly degenerate modes is determined through the beat pattern emerging from them.

In this paper we will analyze the propagation of the angular spectrum of the electromagnetic field through a finite length uniaxial crystal. We solve the boundary conditions of the fields at an interface of an isotropic medium and an uniaxial anisotropic medium with the optical axis in an arbitrary direction and soon after we choose the optical axis in a plane formed by the direction of propagation (z-axis) and the x-axis . We show how the couplings occur between the components of the field and in what situations we can give a vector or scalar treatment for the propagation, Comment: 8 pages, 9 figures

I discuss the strong link between the transmission line (TL) equation and the TL circuit model for the charging of an electrolyte-filled pore of finite length. In particular, I show how Robin and Neumann boundary conditions to the TL equation, proposed by others on physical grounds, also emerge in the TL circuit subject to a stepwise potential. The pore relaxes with a timescale $\tau$, an expression for which consistently follows from the TL circuit, TL equation, and from the pore's known impedance. An approximation to $\tau$ explains the numerically determined relaxation time of the stack-electrode model of Lian et al. [Phys. Rev. Lett. 124, 076001 (2020), arXiv:1911.09924]., Comment: 5 pages, 3 figures

A central problem in Binary Hypothesis Testing (BHT) is to determine the optimal tradeoff between the Type I error (referred to as false alarm) and Type II (referred to as miss) error. In this context, the exponential rate of convergence of the optimal miss error probability -- as the sample size tends to infinity -- given some (positive) restrictions on the false alarm probabilities is a fundamental question to address in theory. Considering the more realistic context of a BHT with a finite number of observations, this paper presents a new non-asymptotic result for the scenario with monotonic (sub-exponential decreasing) restriction on the Type I error probability, which extends the result presented by Strassen in 2009. Building on the use of concentration inequalities, we offer new upper and lower bounds to the optimal Type II error probability for the case of finite observations. Finally, the derived bounds are evaluated and interpreted numerically (as a function of the number samples) for some vanishing Type I error restrictions.

Let F be a non-Archimedean locally compact field of residue characteristic p, let G be an inner form of GL(n,F) with n>0, and let l be a prime number different from p. We describe the block decomposition of the category of finite length smooth representations of G with coefficients in an algebraically closed field of characteristic l. Unlike the case of complex representations of an arbitrary p-adic reductive group and that of l-modular representations of GL(n,F), several non-isomorphic supercuspidal supports may correspond to the same block. We describe the (finitely many) supercuspidal supports corresponding to a given block. We also prove that a supercuspidal block is equivalent to the principal (that is, the one which contains the trivial character) block of the multiplicative group of a suitable division algebra, and we determine those irreducible representations having a nontrivial extension with a given supercuspidal representation of G., Comment: in French language. Annales de l'Institut Fourier, Association des Annales de l'Institut Fourier, A para{\^i}tre

Constrained codes are used to eliminate error-prone patterns in various practical systems. Recently, we introduced efficient binary symmetric lexicographically-ordered constrained (LOCO) codes and asymmetric LOCO (A-LOCO) codes to increase density in magnetic recording systems and lifetime in Flash systems by eliminating the relevant detrimental patterns. Due to their application, LOCO and A-LOCO codes are associated with level-based signaling. Studying the power spectrum of a random signal with certain properties is principal for any storage or transmission system. In this paper, we first modify a framework from the literature in order to introduce a method to derive the power spectrum of a sequence of constrained data associated with level-based signaling. We apply our method to infinitely long sequences satisfying symmetric and asymmetric constraints. Next, we show how to generalize the method such that it works for a stream of finite-length codewords. We use the generalized method to devise closed forms for the spectra of finite-length LOCO and A-LOCO codes from their transition diagrams. Our LOCO and A-LOCO spectral derivations can be performed for any code length and can be extended to other constrained codes. We plot these power spectra, and discuss various important spectral properties for both LOCO and A-LOCO codes., Comment: 30 pages (single column), 12 figures, submitted to the IEEE Transactions on Communications (TCOM)

We consider sparse superposition codes (SPARCs) over complex AWGN channels. Such codes can be efficiently decoded by an approximate message passing (AMP) decoder, whose performance can be predicted via so-called state evolution in the large-system limit. In this paper, we mainly focus on how to use concatenation of SPARCs and cyclic redundancy check (CRC) codes on the encoding side and use list decoding on the decoding side to improve the finite-length performance of the AMP decoder for SPARCs over complex AWGN channels. Simulation results show that such a concatenated coding scheme works much better than SPARCs with the original AMP decoder and results in a steep waterfall-like behavior in the bit-error rate performance curves. Furthermore, we apply our proposed concatenated coding scheme to spatially coupled SPARCs. Besides that, we also introduce a novel class of design matrices, i.e., matrices that describe the encoding process, based on circulant matrices derived from Frank or from Milewski sequences. This class of design matrices has comparable encoding and decoding computational complexity as well as very close performance with the commonly-used class of design matrices based on discrete Fourier transform (DFT) matrices, but gives us more degrees of freedom when designing SPARCs for various applications., Comment: 12 pages, 8 figures, revised