Increasing Block Length Research Articles

Performance Analysis for Reconfigurable Intelligent Surface Assisted MIMO Systems

This paper investigates the maximal achievable rate for a given maximal error probability, and blocklength for the reconfigurable intelligent surface (RIS) assisted multiple-input and multiple-output (MIMO) system. The result consists of a finite blocklength and finite alphabet constraints channel coding achievability and converse bounds based on the Berry-Esseen theorem, the Mellin transform and the closed-form expression of the mutual information and the unconditional variance. The numerical evaluation shows a fast speed of convergence to the maximal achievable rate as the blocklength increases and also proves that the channel variance is a sound measurement of the backoff from the maximal achievable rate due to finite blocklength.

Performance Analysis of Multiple-Antenna Ambient Backscatter Systems at Finite Blocklengths

This paper analyzes the maximal achievable rate for a given blocklength and maximal error probability over a multiple-antenna ambient backscatter channel. The result consists of a finite blocklength channel coding achievability bound and a converse bound for the legacy system with finite alphabet constraints and multiple-input-multiple-output based on the Neyman-Pearson test, the Berry-Esseen theorem, and the Mellin transform. Then, we derive the closed-form expression of the mutual information and the information variance to reduce the complexity of the computation. By applying the low-complexity ML detection, the relation between the maximal error probability of the RF source signal and the average error probability of the tag symbol with respect to the blocklength is proposed. Finally, numerical evaluation of these bounds shows fast convergence to the maximal achievable rate as the blocklength increases and also proves that the information variance is an accurate measure of the backoff from the maximal achievable rate due to finite blocklength.

Application of the method of equivalent message encoding structures to simplify coding complexity

Formulation of the problem. Modern telecommunication technologies make it possible to transmit data over long distances with limitations in the form of low power consumption and low error rate using error correction codes. The use of such codes plays an important role and is necessary to detect and correct errors caused by signal distortion and noise in the communication channel. According to Shannon's channel coding theorem, the probability of error can be arbitrarily small or close to zero if the encoding rate of transmission R is less than or equal to the bandwidth of channel C. Assuming that the bandwidth C is achievable, we can calculate the minimum signal-to-noise power ratio (SNR) to achieve zero error, or an arbitrarily small error called the Shannon limit, while maintaining R ≤ C. This article discusses a method of applying equivalent message encoding structures to construct low-density parity-checking (LDPC) codes. Low-density parity-checking (LDPC) codes are a class of linear block codes in which the complexity of iterative decoding increases linearly with increasing block length. Standard LDPC codes without modifications are considered to demonstrate the effectiveness of the proposed method, which is expected to provide high encoding speed when transmitting messages with a short block length. The method of obtaining equivalent structures allows: to reduce the computational complexity of encoding and decoding; to provide the possibility of finding a new encoding scheme and evaluating its effectiveness. The validity of the method for obtaining equivalent message encoding structures is evaluated by modeling the bit error rate (BER) of LDPC codes. Purpose. to show the effectiveness of the use of equivalent structures for various methods of compression of transmitted information, to minimize the complexity of encoding, while maintaining energy efficiency, correcting ability and data transfer rate. Results. A method is considered for obtaining equivalent message element encoding structures that can be used to create more LDPC codes for data transmission applications with a short block length. The cascade principle of constructing an equivalent generator and a parity check matrix was analyzed, which also leads to minimizing the computational complexity of the encoder and decoder. An equivalent structure G can be obtained from cascading two (or more) matrices by modifying the second matrix so that it has a unit matrix with the size of the parity check length and a shift to the right by k bits. On the other hand, the equivalent structure H can be obtained by simply cascading directly the second matrix and shifting to the right by k bits. According to the simulation results, the proposed method is adequate, since LDPC codes have the same BER characteristics as codes based on the low density generator matrix (LDGM). During the simulation, it was concluded that the SPC codes (single parity check (single parity check (SPC)) are the most efficient codes (for a given block length), since SPC codes have the smallest interval up to the Shannon limit. Practical significance. The results presented in this article will give a new insight into the development of simple channel coding of LDPC codes of short block length with high encoding speed for future applications with lower power consumption.

Fine-Tuned Polymer Nanoassembly for Codelivery of Chemotherapeutic Drug and siRNA.

Successful clinical application of siRNA to liver-associated diseases reinvigorates the RNAi therapeutics and delivery vectors, especially for anticancer combination therapy. Fine tuning of copolymer-based assembly configuration is highly important for a desirable synergistic cancer cell-killing effect via the codelivery of chemotherapeutic drug and siRNA. Herein, an amphiphilic triblock copolymer methoxyl poly(ethylene glycol)-block-poly(L-lysine)-block-poly(2-(diisopropyl amino)ethyl methacrylate) (abbreviated as mPEG-PLys-PDPA or PLD) consisting of a hydrophilic diblock mPEG-PLys and a hydrophobic block PDPA is synthesized. Three distinct assemblies (i.e., nanosized micelle, nanosized polymersome, and microparticle) are acquired, along with the increase in PDPA block length. Furthermore, the as-obtained polymersome can efficiently codeliver doxorubicin hydrochloride (DOX) as a hydrophilic chemotherapeutic model and siRNA against ADP-ribosylation factor 6 (siArf6) as an siRNA model into cancer cell via lysosomal pH-triggered payload release. PC-3 prostate cell is synergistically killed by the DOX- and siArf6-coloading polymersome (namely PLD@DOX/siArf6). PLD@DOX/siArf6 may serve as a robust nanomedicine for anticancer therapy.

Efficient Partial Rewind of Successive Cancellation-Based Decoders for Polar Codes

The successive cancellation (SC) process in which symbols are decoded sequentially by processing some intermediate information is an essential component of various decoding algorithms used for polar codes and their variants. In some decoding schemes, we may need to redo this process from some specific symbol or from the first symbol. This operation is called rewinding. Rewinding the SC process seems trivial if we have access to all intermediate log-likelihood ratios (LLRs) and partial sums. However, as the block length increases, retaining all of the intermediate information becomes inefficient and impractical. Rewinding the SC process in a memory-efficient way is a problem that we address in this paper. As we store a fraction of all the intermediate information in the memory-efficient scheme, we may not be able to rewind the SC process to the target symbol index. The reason is that some of the stored intermediate information needed to decode the target symbol may have been overwritten. To recompute the lost information, we may need to rewind the process further. Before proposing the formal scheme for the rewinding process, we explore the known properties of the SC process based on the binary representation of the bit indices. Then, we introduce a new operator used for grouping the bit indices. This special grouping helps us in finding the closest bit index to the target index for rewinding. We also analytically prove that this approach gives access to the untouched intermediate information stored in the memory which is essential in resuming the SC process. Finally, we adapt the proposed approach to multiple rewinds and apply it to SC-flip decoding and shifted-pruning-based list decoding. The numerical evaluation of the proposed solution shows a significant reduction of ≥50% in the complexity of the additional decoding attempts at medium and high SNR regimes for SC-flip decoding and less for shifted-pruning based list decoding.

An Information-Theoretic Perspective on Successive Cancellation List Decoding and Polar Code Design

This work identifies information-theoretic quantities that are closely related to the required list size on average for successive cancellation list (SCL) decoding to implement maximum-likelihood decoding over general binary memoryless symmetric (BMS) channels. It also provides upper and lower bounds for these quantities that can be computed efficiently for very long codes. For the binary erasure channel (BEC), we provide a simple method to estimate the mean accurately via density evolution. The analysis shows how to modify, e.g., Reed-Muller codes, to improve the performance when practical list sizes, e.g., <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$L\in {[{8, 1024}]}$ </tex-math></inline-formula> , are adopted. Exemplary constructions with block lengths <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$N\in \{128,512\}$ </tex-math></inline-formula> outperform polar codes of 5G over the binary-input additive white Gaussian noise channel. It is further shown that there is a concentration around the mean of the logarithm of the required list size for sufficiently large block lengths, over discrete-output BMS channels. We provide the probability mass functions (p.m.f.s) of this logarithm, over the BEC, for a sequence of the modified RM codes with an increasing block length via simulations, which illustrate that the p.m.f.s concentrate around the estimated mean.

In situ photo‐crosslinked hydrogels prepared from acrylated 4‐arm‐poly(ethylene glycol)‐poly(ε‐caprolactone) block copolymers for local cancer therapy

AbstractAmphiphilic block copolymers were synthesized by ring‐opening polymerization of ε‐caprolactone (ε‐CL) using 4‐arm poly(ethylene glycol) (4aPEG) as macroinitiator. 4aPEG and 4aPEG‐PCL copolymers were end functionalized by introducing acrylic groups, and characterized using NMR, GPC, FT‐IR and DSC analyses. Photo‐crosslinked hydrogels were prepared by irradiation of acrylated polymer solutions under visible light (405 nm), using lithium phenyl‐2,4,6‐trimethylbenzoy‐lphosphinate (LAP) as a photoinitiator. In situ gelation was achieved by subcutaneous injection of LAP containing copolymer solution into the abdomen of mice, followed by exposure to visible light. The hydrogels exhibit highly porous structure, high swelling up to 3300%, and excellent biocompatibility. The swelling ratio decreases with increase of poly(ɛ‐caprolactone) (PCL) block length and polymer concentration of hydrogels. Doxorubicin hydrochloride (DOX·HCl) was loaded in hydrogels by soaking dried gel in a DOX solution. The drug loading efficiency is dependent on the swelling performance, reaching a maximum of 94.3%. In vitro drug release studies showed a burst release for the first 6 h, followed by a slower release up to 82% at 28 days. The release rate decreased with increase of hydrophobic block length or polymer concentration of hydrogels. Higher anti‐cancer activity on A549 lung cancer cells was obtained for hydrogels with higher drug concentration, and shorter PCL block length. Therefore, 4aPEG‐PCL hydrogels with outstanding biocompatibility, in situ gelation and prolonged drug release could be very promising for long‐term local cancer therapy.

Sliding dynamics of ring on a fixed rod-like block copolymer in rotaxane: Molecular dynamics simulations vs Lifson-Jackson formula

Rotaxane is a mechanically interlocked molecule in which ring chains are threaded onto a linear axial polymer chain, and a typical feature of rotaxane is that the ring chains can slide along the axial chain. In this study, molecular dynamics simulations and Lifson-Jackson formula are performed to examine the sliding dynamics of ring chain threaded on a fixed rod-like AB block copolymer consisting of A and B blocks in which the A-block composed of NA monomers is attractive to the ring chain, while the B-block with NB monomers is repelled from the ring chain. From a series of studies on ring sliding along the AB block copolymer with the repeat unit of ANABNB, we find that the sliding dynamics of ring relies strongly on the block length of (NA+NB), the volume fraction fa of A-block as well as the block-ring interaction ε. First, the sliding diffusion coefficient D of ring decreases sharply by several orders magnitude with an increase in block length or block-ring interaction strength. Next, the sliding dynamics has a strongly non-monotonic dependence on fa, and the slowest diffusion motion occurs for ring threaded onto the symmetric block copolymer with fa=0.5. From the view of free energy potential, both the width of free energy potential well and the height of free energy potential barrier govern the sliding diffusion behavior of ring chain. According to potential of mean force (PMF) of ring sliding along the fixed rod-like block copolymer, we find that our results are good agreement with the theoretical analysis using the Lifson-Jackson formula. Our investigation can provide a simple as well as practical model to study the diffusion of particle in a periodic medium, which is one of the interesting problems in many different fields of sciences, such as physics, chemistry and biology.

Toward a Green Secure Relay System for Mission-Critical IoT: Hybrid Duplex Relay Selection and Resource Allocation in the Finite Block Length Regime

In this paper, we investigate the physical layer security of a relay system toward secure and green mission-critical Internet of Things, in the finite block length regime, which was hardly considered in the literature. Closed-form expressions for statistical secrecy throughput of full-duplex (FD) and half-duplex (HD) relay systems are respectively derived and verified by simulation results. To maximize the secrecy throughput derived, joint optimization of block length and transmit powers at source and relay is conducted, and a hybrid duplex relay selection (HyDRS) scheme is also proposed, where a relay out of multiple candidates and its duplex mode is selected. Simulation results demonstrate the following findings. a) Together with the HyD relaying scheme, the proposed joint power allocation and block length adaptation scheme achieves much higher secrecy throughput than the conventional sole FD/HD mode relay systems. b) With the proposed HyDRS scheme, a higher degree of freedom in transmission is achieved than the single relay candidate scenario, leading to higher secrecy throughput and energy efficiency. c) It is revealed that increasing block length or transmit power may not always make a positive contribution to secrecy throughput and energy efficiency.

Biocompatibility, drug release, and anti‐tumor effect of pH‐sensitive micelles prepared from poly(2‐ethyl‐2‐oxazoline)‐poly(DL‐lactide) block copolymers

AbstractVarious ratios PEOz‐PDLLA diblock copolymers were synthesized through ring‐opening polymerization of DL‐lactide initiated by monohydroxyl terminated poly(2‐ethyl‐2‐oxazoline) (PEOz‐OH). The chemical composition and molar mass of the resulting copolymers were determined by using NMR and GPC. Spherical micelles with a diameter from 104 to 136 nm were obtained via self‐assembly of PEOz‐PDLLA in water, as evidenced by TEM and DLS. The CMC of copolymers was well below 0.01 mg/mL, and showed a decreasing trend with increase of PDLLA block length. A two‐step procedure was applied to encapsulate curcumin taken as a hydrophobic model drug. Copolymers with longer PDLLA block exhibit enhanced drug loading capacity. In vitro drug release was carried out in phosphate buffered saline (PBS) at physiological and slightly acidic pH values. A pH‐sensitive biphasic drug release behavior was detected with an initial burst release followed by slower prolonged release. Lower pH or shorter PDLLA block length leads to higher drug release rate because of faster degradation of micelles. Hemo‐ and cytocompatibility studies illustrated the excellent biocompatibility of PEOz‐PDLLA micelles. MTT assay showed a significant cytotoxicity of curcumin‐loaded micelles against A549 lung cancer cells. Therefore, it can be inferred that PEOz‐PDLLA block copolymers with outstanding biocompatibility, controllable drug loading performance, and prolonged drug release present a good potential as nano‐carrier of hydrophobic drugs.

Self-assembly, pH-responsibility and controlled release of doxorubicin of PDEAEMA-PEG-PDEAEMA triblock copolymers: effects of PEG length

Effects of poly(ethylene glycol) (PEG) block length on the self-assembly of a series of pH-sensitive poly(N,N-diethylaminoethyl methacrylate)m-PEGn-poly(N,N-diethylaminoethyl methacrylate)m triblock copolymers (PDEAEMAm-PEGn-PDEAEMAm) have been studied. The synthesized triblock copolymers have an almost fixed PDEAEMA block length (m ≈ 65) and varying PEG block lengths (n = 11, 20, 89 or 134). The acid–base titration results show that the pKa value of the block copolymer shifts from 6.84 to 7.08 when the PEG block length increases from 11 to 134, indicating that the pH-sensitivity of the triblock copolymer can be adjusted through changing the PEG block length. With the increase of the hydrophilic PEG block length, the critical micelle concentration value of the triblock copolymer obtained from fluorescence spectroscopy changes from 5.50 × 10–3 to 13.23 × 10–3 mg mL−1. The block copolymers can self-assemble into the micelles in PBS solution at pH 7.4, and the average size of the self-assembly decreases from 178 nm to 45 nm with the increase of the PEG block length as determined by dynamic light scattering. The block copolymers show great biocompatibility in the cytotoxicity assay. Results from these triblock copolymers in the drug-controlled release indicate that the release rate of doxorubicin-loaded micelles at pH 5.0 is faster than that at pH 7.4, and the cumulative drug release in 48 h at pH 5.0 increases from 70.4% to 89.8% with the decrease of the PEG block length. Accordingly, this PDEAEMA65-PEGn-PDEAEMA65 copolymer is an excellent carrier for controllable drug delivery and release.

Poly(Ethylene Glycol)-b-Poly(D,L-Lactide) Nanoparticles as Potential Carriers for Anticancer Drug Oxaliplatin.

Nanoparticles based on biocompatible methoxy poly(ethylene glycol)-b-poly(D,L-lactide) (mPEG113-b-P(D,L)LAn) copolymers as potential vehicles for the anticancer agent oxaliplatin were prepared by a nanoprecipitation technique. It was demonstrated that an increase in the hydrophobic PLA block length from 62 to 173 monomer units leads to an increase of the size of nanoparticles from 32 to 56 nm. Small-angle X-ray scattering studies confirmed the “core-corona” structure of mPEG113-b-P(D,L)LAn nanoparticles and oxaliplatin loading. It was suggested that hydrophilic oxaliplatin is adsorbed on the core-corona interface of the nanoparticles during the nanoprecipitation process. The oxaliplatin loading content decreased from 3.8 to 1.5% wt./wt. (with initial loading of 5% wt./wt.) with increasing PLA block length. Thus, the highest loading content of the anticancer drug oxaliplatin with its encapsulation efficiency of 76% in mPEG113-b-P(D,L)LAn nanoparticles can be achieved for block copolymer with short hydrophobic block.

Synthesis of ABA-type double hydrophilic amphiphilic PU-based block copolymers of poly(N-Vinylpyrrolidone) and poly(N-isopropylacrylamide) via click chemistry

Double hydrophilic ABA-type amphiphilic polyurethane (PU)-based poly(N-vinylpyrrolidone) (PNVP)-b-PU-b-PNVP and poly(N-isopropylacrylamide) (PNIPAM)-b-PU-b-PNIPAM triblock copolymers have successfully been synthesized via the combination of the step-growth polymerization, reversible addition-fragmentation chain transfer (RAFT) polymerization and azide-alkyne click reaction. All polymers are characterized by 1H NMR, FTIR, and gel permeation chromatography. The cmcs of PNVP-b-PU-b-PNVP block copolymers increase with increase in PNVP block length: 0.0019 mg/mL for PNVP39-b-PU-b-PNVP39 and 0.005 mg/mL for PNVP68-b-PU-b-PNVP68. The iron-chelating ability and the reducing power of PNVP68-b-PU-b-PNVP68 are superior to that of PNVP owing to the presence of urethane moiety of PU block in copolymer. The LCST of PNIPAM-b-PU-b-PNIPAM are lower than that of PNIPAM (33 °C): 23.5 and 25.5 °C for PNIPAM42-b-PU-b-PNIPAM42 and PNIPAM66-b-PU-b-PNIPAM66, respectively.

Preparation of Doxorubicin-Loaded Amphiphilic Poly(D,L-Lactide-Co-Glycolide)-b-Poly(N-Acryloylmorpholine) AB2 Miktoarm Star Block Copolymers for Anticancer Drug Delivery.

Owing to their unique topology and physical properties, micelles based on miktoarm amphiphilic star block copolymers play an important role in the biomedical field for drug delivery. Herein, we developed a series of AB2-type poly(D,L-lactide-co-glycolide)-b-poly(N-acryloyl morpholine) (PLGA-b-PNAM2) miktoarm star block copolymers by reversible addition–fragmentation chain–transfer polymerization and ring-opening copolymerization. The resulting miktoarm star polymers were investigated by 1H NMR spectroscopy and gel permeation chromatography. The critical micellar concentration value of the micelles increases with an increase in PNAM block length. As revealed by transmission electron microscopy and dynamic light scattering, the amphiphilic miktoarm star block copolymers can self-assemble to form spherical micellar aggregates in water. The anticancer drug doxorubicin (DOX) was encapsulated by polymeric micelles; the drug-loading efficiency and drug-loading content of the DOX-loaded micelles were 81.7% and 9.1%, respectively. Acidic environments triggered the dissociation of the polymeric micelles, which led to the more release of DOX in pH 6.4 than pH 7.4. The amphiphilic PLGA-b-PNAM2 miktoarm star block copolymers may have broad application as nanocarriers for controlled drug delivery.

Self-healing Polyurethane Elastomer Based on Molecular Design: Combination of Reversible Hydrogen Bonds and High Segment Mobility

Polyurethane (PU) belongs to a class of special polymeric materials with hydrogen bonds, which has the potential for self-healing ability. In the present work, by introducing polypropylene glycol (PPG) blocks with high segment mobility and different block lengths on the ends of PU chains, the PUs with adjustable self-healing ability were successfully obtained. The self-healing ability of the PUs firstly increases with the increase of the PPG block lengths, but then decreases. This phenomenon can be attributed to the combined effects of the density of hydrogen bonds and the mobility of PPG segments. At first, the increase of the PPG block length leads to the improvement of mobility of PU chains, which is beneficial for the enhancement of the self-healing. However, the further increase of the PPG block length results in the reduction in the hydrogen bond density, finally leading to the decrease of the self-healing ability of the PUs.

Self-assembled micelles prepared from bio-based hydroxypropyl methyl cellulose and polylactide amphiphilic block copolymers for anti-tumor drug release

Fully bio-based amphiphilic diblock copolymers were synthesized from hydroxypropyl methyl cellulose (HPMC) and amino-terminated poly(l-lactide) (PLLA) or poly(l-lactide-co-dl-lactide) (PLA) by reductive amination. The resulting HPMC-PLLA and HPMC-PLA copolymers with various hydrophobic block lengths were characterized by NMR, DOSY-NMR and FT-IR. Micelles were obtained by self-assembly of copolymers in aqueous medium. The micelles are spherical in shape, and the micelle size ranges from 150 to 180 nm with narrow distribution. The critical micelle concentration decreases with increasing PLA block length. Paclitaxel was loaded in micelles. Enhanced drug loading is obtained with increase of PLA block length. A biphasic release profile is observed with a burst of 40% followed by slower release up to 80%. MTT assay indicates the good cytocompatibility of HPMC-PLA micelles. SRB assay shows a significant cytotoxicity of paclitaxel-loaded micelles against SK-BR-3cells. It is thus concluded that bio-based HPMC-PLA block copolymers could be promising nano-carrier of anti-tumor drugs.

Effect of chain segment length on crystallization behaviors of poly(l-lactide-b-ethylene glycol-b-l-lactide) triblock copolymer

The poly(l-lactide-b-ethylene glycol-b-l-lactide) (PLLA-PEG-PLLA) triblock copolymers with different chain segment length are fabricated by ring-opening polymerization. The structure, molecular weight, and crystallization behaviors of the triblock copolymers are characterized by Fourier transform infrared, nuclear magnetic resonance spectroscopy, gel permeation in chromatography, X-ray diffraction, differential scanning calorimetry, and polarizing optical microscopy (POM). The results show that the increase of block length is beneficial to improve its crystallization. In addition, the triblock copolymer exhibits a double crystallization phenomenon. The POM results indicate that PEG and PLLA chains of the copolymer crystallize in their respective crystallization temperature regions. The growth rate of the PLLA spherocrystal decreases and the dendritic spherocrystals appear with increasing the PEG chain length when the PLLA chain of the copolymer is isothermal crystallized at 80°C and PLLA chain length is constant. The growth rate of the PEG spherocrystal decreases and the spherocrystal morphology changes little with increasing PLLA chain length when the PEG chain is isothermal crystallized at 25°C and the length of PEG chain remained unchanged.

Crystallization and Properties of Poly(lactide)/Poly(δ-valerolactone) Alternating Supramolecular Copolymers Adjusted by Stereocomplexation.

The crystallization behavior of a series of synthesized polylactide (PLA)/poly(δ-valerolactone) (PVL) supramolecular copolymers with 2-ureido-4[1H]-pyrimidinone (UPy) groups is investigated by differential scanning calorimetry and X-ray diffraction. The stereocomplexation of PLA-based supramolecular polymers (SMPs) is strongly related to the block length, L/D ratios, and the UPy groups. Both the increase of the PLA block length and the self-complementary hydrogen bonding of the UPy end groups restrain the crystallization of the PVL blocks. The stereocomplexation of PLA-SMPs is greatly promoted by UPy groups, while the homocrystallization of PLA is constrained. The dynamic mechanical analysis indicated that the enhanced stereocomplexation would lead to higher thermal resistance and mechanical properties of PLA-based SMPs.

Multi-block versus random quaternary ammonium Poly(arylene ether sulfone) membrane dependent water and alcohol mass uptake, directionally-dependent swelling and ion conductivity, and alcohol transport

Quaternary ammonium poly(arylene ether sulfone) copolymer random and multi-block ionomers were synthesized using multiple condensation reactions. Hydrophilic and hydrophobic block-length relationships were investigated with respect to directionally-dependent water swelling, hydroxyl conductivity, percolation-dependent properties, and alcohol transport. 1H nuclear magnetic resonance was used to evaluate brominated multi-block poly(arylene ether sulfone) composition, degree of functionalization, and ion-exchange capacity (IEC). These highly aminated ionomers did not display any counterion condensation associated with their conductivity as predicted by Oosawa-Manning Counterion Condensation Theory. Water-swollen quaternary ammonium poly(arylene ether sulfone) copolymer random and multi-block ionomers; and Nafion 117 membrane conductivity was modeled using Percolation Theory. In general, multi-block ionomer in-plane hydroxide conductivity was greater than its randomly functionalized counterpart at a similar IEC. Multi-block ionomer films with the largest hydrophilic block length (24k) exhibited a hydroxide conductivity of 62.1 mS/cm. An equivalent random copolymer's conductivity was 1.25 times lower. Multi-block and random copolymer's in-plane conductivity was 23.5% lower than its through-plane conductivity at an IEC greater than 2.02 meq/g. This decrease was strongly coupled with its swelling ratio and water uptake (WU). Increased swelling and water dilutes the available charge carriers responsible for through-plane conductivity. A percolation threshold at an IEC of 1.75 was observed for the random copolymer. Its maximum WU was 223 wt%. The multi-block ionomer's WU ranged between 172 wt% and 78.6 wt% at a similar IEC. Swelling suppression at high IEC was attributed to the sequential hydrophilic-hydrophobic block architecture. Multi-block ionomers with smaller hydrophilic block lengths appeared to inhibit alcohol transport more effectively than larger ones at the same IEC. Increasing block length led to greater water and alcohol uptake that was related to ion-domain size, alcohol polarity, and ionomer solubility parameter. Smaller hydrophilic block size was more effective at decreasing alcohol permeation at a similar ion-group concentration. This was attributed to reduced ion-domain cluster size not achievable with larger hydrophilic multiblock ionomers. These results suggest that block length has an important role in controlling ionomer swelling, and ion and alcohol transport, which is critical to fuel cells, and solid-state electrochemical devices.

On Recovery of Block Sparse Signals via Block Compressive Sampling Matching Pursuit

Compressive sampling matching pursuit (CoSaMP) is an efficient reconstruction algorithm for sparse signal. When the signal is block sparse, i.e., the non-zero elements are presented in clusters, some block sparse reconstruction algorithms have been proposed accordingly. In this paper, we present a new block algorithm based on CoSaMP, called block compressive sampling matching pursuit (BlockCoSaMP). Compared with CoSaMP algorithm, the proposed algorithm shows improved performance when sparse signal is presented in block form. Restricted isometry property (RIP) of measurement matrix is an effective tool for analyzing the performance of the CS algorithm, and Block restricted isometry property (Block RIP) is the extension of traditional RIP. Based on the Block RIP, we derive the sufficient condition to guarantee the convergence of Block-CoSaMP algorithm. In addition, the number of required iterations is obtained. Finally, simulation experiments show that with the increase of block length, the performance of Block-CoSaMP algorithm approaches to that of block subspace pursuit (Block-SP) algorithm. When the block length and sparsity are small, the performance of Block-CoSaMP algorithm is better than that of the CoSaMP, l 2 /l 1 norm and block orthogonal matching pursuit (BOMP) algorithms. Especially, when compared with CoSaMP and l 2 /l 1 norm algorithms, the proposed algorithm exhibits more obvious performance gain.