Short Block Length Research Articles

Quasi-Cyclic Protograph-Based Raptor-Like LDPC Codes for Short Block-Lengths

Protograph-based Raptor-like low-density parity-check codes (PBRL codes) are a family of easily encodable rate-compatible low-density parity-check (LDPC) codes. PBRL codes have an excellent performance across all design rates. Quasi-cyclic (QC) PBRL code families permit high-speed decoder implementations. PBRL codes designed thus far, for both long and short block-lengths, have been based on optimizing the iterative decoding threshold of the protograph of the PBRL family at various design rates. This paper introduces a design method to obtain better QC PBRL code families at short block-lengths (of a few hundred bits) for low frame error rate (FER) requirements. We first select a protomatrix for the highest design rate. To add a new row to lower the rate, we keep all the previously obtained rows of the PBRL protomatrix fixed and select the new row that maximizes an upper bound on the minimum distance of any QC-LDPC code that can be obtained from the protomatrix. The new QC PBRL code families outperform the original PBRL codes at short block-lengths by providing a significantly better low-FER performance. The standard approach to computing the aforementioned upper bounds requires complexity that grows exponentially with the size of the protomatrix. However, we show that the structure of the PBRL protomatrix lets us obtain the upper bounds with complexity that grows only linearly with the size of the PBRL protomatrix. Using the complexity reduction results, we also establish an equivalence between the exhaustive search to design a new row for the PBRL protomatrix according to the new design method and an integer linear program.

Introducing Enumerative Sphere Shaping for Optical Communication Systems With Short Blocklengths

Probabilistic shaping based on constant composition distribution matching (CCDM) has received considerable attention as a way to increase the capacity of fiber optical communication systems. CCDM suffers from significant rate loss at short blocklengths and requires long blocklengths to achieve high shaping gain, which makes its implementation very challenging. In this paper, we propose to use enumerative sphere shaping (ESS) and investigate its performance for the nonlinear fiber optical channel. ESS has lower rate loss than CCDM at the same shaping rate, which makes it a suitable candidate to be implemented in real-time high-speed optical systems. In this paper, we first show that finite blocklength ESS and CCDM exhibit higher effective signal-to-noise ratio than their infinite blocklength counterparts. These results show that for the nonlinear fiber optical channel, large blocklengths should be avoided. We then show that for a 400 Gb/s dual-polarization 64-QAM WDM transmission system, ESS with short blocklengths outperforms both uniform signaling and CCDM. Gains in terms of both bit-metric decoding rate and bit-error rate are presented. ESS with a blocklength of 200 is shown to provide an extension reach of about 200 km in comparison with CCDM with the same blocklength. The obtained reach increase of ESS with a blocklength of 200 over uniform signaling is approximately 450 km (approximately 19%)

Fine Asymptotics for Universal One-to-One Compression of Parametric Sources

Universal source coding at short blocklengths is considered for an i.i.d. exponential family of distributions. The Type Size code has previously been shown to be optimal up to the third-order rate for universal compression of all memoryless sources over finite alphabets. The Type Size code assigns sequences ordered based on their type class sizes to binary strings ordered lexicographically. To generalize this type class approach for parametric sources, a natural scheme is to define two sequences to be in the same type class if and only if they are equiprobable under any model in the parametric class. This natural approach, however, is shown to be suboptimal. A variation of the Type Size code is introduced, where type classes are defined based on neighborhoods of minimal sufficient statistics. The asymptotics of the overflow rate of this variation are derived and a converse result establishes its optimality up to the third-order term.

Divergence-Optimal Fixed-to-Fixed Length Distribution Matching With Shell Mapping

Distribution matching (DM) transforms independent and Bernoulli(1/2) distributed bits into a sequence of output symbols with a desired distribution. A fixed-to-fixed length, invertible DM architecture based on shell mapping (SM) is presented. It is shown that SM for DM (SMDM) is the optimum DM for the informational divergence metric and that finding energy optimal sequences is a special case of divergence minimization. Additionally, it is shown how to find the required SM weight function to approximate arbitrary output distributions. SMDM is combined with probabilistic amplitude shaping to operate close to the Shannon limit. SMDM exhibits excellent performance for short blocklengths as required by ultra-reliable low-latency applications. SMDM outperforms constant composition DM by 0.7 dB when used with 64-QAM at a spectral efficiency of 3 bits/channel use and a 5G low-density parity-check code with a short blocklength of 192 bits.

Efficient error-correcting codes in the short blocklength regime

The design of block codes for short information blocks (e.g., a thousand or less information bits) is an open research problem that is gaining relevance thanks to emerging applications in wireless communication networks. In this paper, we review some of the most promising code constructions targeting the short block regime, and we compare them with both finite-length performance bounds and classical error-correction coding schemes. The work addresses the use of both binary and high-order modulations over the additive white Gaussian noise channel. We will illustrate how to effectively approach the theoretical bounds with various performance versus decoding complexity tradeoffs.

Analysis of the Joint Viterbi Detector/Decoder (JVDD) Over a Coded AWGN/ISI System ss an LDPC Alternative

The joint Viterbi detector/decoder (JVDD) has been proposed as an alternative to the powerful and ubiquitous low-density parity check (LDPC) coding schemes, that are used in the majority of channel coding applications today. At shorter block lengths, the JVDD is able to outperform the state-of-the-art LDPC decoder that can be found in many of today’s systems, from deep-space communications to the digital video broadcasting standard, to the advanced television standard committee 3.0. Researchers have developed the tools to analyze the performance of the LDPC decoder, which is known as the sum-product algorithm or message passing algorithm. These tools include density evolution (DE) and extrinsic information transfer (EXIT) charts. To date, no similar such analysis exists for the JVDD. In the current paper we perform a similar preliminary analysis on the JVDD algorithm akin to what DE and EXIT charts are for the LDPC decoder. The current new analysis of the JVDD allows prediction of its probability of error based on the probability distribution functions of the metrics used within the algorithm. Our analysis plays a similar role to the abovementioned tools developed for the LDPC decoder: it allows us to predict the performance of the JVDD under various conditions (such as varying SNR’s, thresholds, and block lengths), it improves our understanding of the JVDD algorithm and the match against Monte-Carlo simulations verifies our assumptions on the main error-causing mechanisms within the JVDD.

Short Block-Length Codes for Ultra-Reliable Low Latency Communications

This article reviews state of the art channel coding techniques for URLLC. The stringent requirements of URLLC services, such as ultrahigh reliability and low latency, have made it the most challenging feature of 5G of mobile networks. The problem is even more challenging for services beyond the 5G promise, such as tele-surgery and factory automation, which require latencies less than 1ms and packet error rates as low as 10-9. This article provides an overview of channel coding techniques for URLLC and compares them in terms of performance and complexity. Several important research directions are identified and discussed in more detail.

Joint Coding and Adaptive Image Transmission Scheme Based on DP-LDPC Codes for IoT Scenarios

For wireless image communication in the Internet of Things (IoT) scenarios, fast and low error coding and transmission mechanisms are imperative. The joint source-channel coding scheme based on the double protograph low-density parity-check (DP-LDPC) codes would be a potential candidate due to the low complexity and good error performance. However, the error floor performance of DP-LDPC codes may deteriorate for source sequences with higher source probabilities or shorter block lengths. This paper aims to improve the traditional DP-LDPC image transmission system for the IoT scenarios from the following aspects. First, a joint optimization method of finite-length DP-LDPC codes is proposed to reduce the error floor while keeping satisfactory waterfall region performance. Second, an improved rate allocation strategy based on the fuzzy logic control is adopted to further improve the transmission reliability of the proposed short block length DP-LDPC codes. This scheme may offer some new solutions for the IoT image communication. The simulation results indicate the effectiveness of the proposed methods.

Optimizing Resource Allocation in the Short Blocklength Regime for Ultra-Reliable and Low-Latency Communications

In this paper, we aim to find the global optimal resource allocation for ultra-reliable and low-latency communications (URLLC), where the blocklength of channel codes is short. The achievable rate in the short blocklength regime is neither convex nor concave in bandwidth and transmit power. Thus, a non-convex constraint is inevitable in optimizing resource allocation for URLLC. We first consider a general resource allocation problem with constraints on the transmission delay and decoding error probability, and prove that a global optimal solution can be found in a convex subset of the original feasible region. Then, we illustrate how to find the global optimal solution for an example problem, where the energy efficiency (EE) is maximized by optimizing antenna configuration, bandwidth allocation, and power control under the latency and reliability constraints. To improve the battery life of devices and EE of communication systems, both uplink and downlink resources are optimized. The simulation and numerical results validate the analysis and show that the circuit power is dominated by the total power consumption when the average inter-arrival time between packets is much larger than the required delay bound. Therefore, optimizing antenna configuration and bandwidth allocation without power control leads to minor EE loss.

Distribution Matching for High Spectral Efficiency Optical Communication With Multiset Partitions

In this paper, we review the concept of multiset-partition-based distribution matching. We then characterize performance over short block lengths of 20, 40, and 80 symbols, and with 16QAM, 64QAM, and 256QAM modulation formats. We note that a 40 symbol distribution matcher length can obtain better than uniform performance, while an 80 symbol distribution matcher can utilize most of the available gain over a wide range of signal-to-noise ratios.

Resource allocation for ultra-reliable low latency communications in sparse code multiple access networks

In this paper, we propose an optimal resource allocation policy for sparse code multiple access (SCMA) networks supporting ultra-reliable low-latency communications (URLLC). The network is assumed to operate with finite blocklength (FBL) codes, which is opposed to the classical information-theoretic works with infinite blocklength (IBL) codes. In particular, we aim at maximizing the average transmission rate in the FBL regime while guaranteeing the transmission reliability. A joint design is proposed, which combines the power allocation with the codebook assignment. The convexity of the corresponding optimization problem is analyzed and an iterative search algorithm is further provided. We study the impact of reliability and short blocklength constraints on the performance of the proposed optimal resource allocation policy through numerical simulations. In addition, we evaluate the FBL performance of the proposed joint design in comparison to the scenario with an IBL assumption.

Effects of chemical composition on the in vitro degradation of micelles prepared from poly(D,L-lactide-co-glycolide)-poly(ethylene glycol) block copolymers

In this work, a series of poly(D,L-lactide-co-glycolide)-poly(ethylene glycol) (PLGA-PEG) diblock copolymers with relatively short PLGA blocks were synthesized by ring-opening polymerization of D,L-lactide and glycolide in the presence of monomethoxy PEG with Mn of 2000. Spherical micelles were obtained by self-assembly of copolymers using direct dissolution method. The degradation of the micelles was investigated under in vitro conditions at 37 °C. The effects of chemical composition on micelle degradation were evaluated from NMR, GPC, DLS and TEM measurements. The molar mass of copolymers constantly decreases during degradation in all cases. The copolymers with longer hydrophobic PLGA blocks exhibit larger molar mass decrease rate since only the PLGA block is degradable. Meanwhile, the molar mass distribution remains almost unchanged, in agreement with random chain cleavage. NMR spectra show that the final degradation products are lactic acid and glycolic acid. A pH decrease is also detected during degradation. The size of the micelle depends on the chemical composition of copolymers. Micelle size is smaller for copolymers with longer hydrophobic PLGA blocks because of more compact core structure. With the hydrolysis of the PLGA blocks, the structure of micelles becomes looser, and the micelle size exhibits a sharp increase after a lag time. At the later stage of degradation, the size of micelles decreases as they become unstable and could collapse. The micelle structure could be clearly distinguished after 45 days degradation for copolymers with longer PLGA blocks, whereas those with shorter PLGA blocks lost the structural integrity. It is also noteworthy that the LA/GA ratio has little effect on the degradation of PLGA-PEG copolymer micelles, which may be related to the amorphous structure of PLGA block and the relatively short block length. These findings should be helpful for the conception of drug delivery systems based on PLGA-PEG micelles.

Improving Network Availability of Ultra-Reliable and Low-Latency Communications With Multi-Connectivity

Ultra-reliable and low-latency communications (URLLC) have stringent requirements on quality-of-service and network availability. Due to path loss and shadowing, it is very challenging to guarantee the stringent requirements of URLLC with satisfactory communication range. In this paper, we first provide a quantitative definition of network availability in the short blocklength regime: the probability that the reliability and latency requirements can be satisfied when the blocklength of channel codes is short. Then, we establish a framework to maximize available range, defined as the maximal communication distance subject to the network availability requirement, by exploiting multi-connectivity. The basic idea is using both device-to-device (D2D) and cellular links to transmit each packet. The practical setup with correlated shadowing between D2D and cellular links is considered. Besides, since processing delay for decoding packets cannot be ignored in URLLC, its impacts on the available range are studied. By comparing the available ranges of different transmission modes, we obtained some useful insights on how to choose transmission modes. Simulation and numerical results validate our analysis, and show that multi-connectivity can improve the available ranges of D2D and cellular links remarkably.

Analysis of short blocklength codes for secrecy

In this paper, we provide secrecy metrics applicable to physical-layer coding techniques with finite blocklengths over Gaussian and fading wiretap channel models and analyze their secrecy performance over several cases of concatenated code designs. Our metrics go beyond some of the known practical secrecy measures, such as bit error rate and security gap, so as to make lower bound probabilistic guarantees on error rates over short blocklengths both preceding and following a secrecy decoder. Our techniques are especially useful in cases where application of traditional information-theoretic security measures is either impractical or simply not yet understood. The metrics can aid both practical system analysis, including cryptanalysis, and practical system design when concatenated codes are used for physical-layer security. Furthermore, these new measures fill a void in the current landscape of practical security measures for physical-layer security coding and may assist in the wide-scale adoption of physical-layer techniques for security in real-world systems. We also show how the new metrics provide techniques for reducing realistic channel models to simpler discrete memoryless wiretap channel equivalents over which existing secrecy code designs may achieve information-theoretic security.

Short block length trellis‐based codes for interference channels

In this study, the authors consider Gaussian interference channels and fading interference channels, and design short block length codes based on trellis-based constructions. For both joint maximum likelihood (JML) decoding and single user minimum distance decoding, they obtain error-rate bounds to assess the code performance. Then they employ the obtained bounds for code design and present several design examples. For the case of quasi-static fading, they note that while the simple version of the derived bound is not sufficiently tight for code search purposes, one can obtain a tight performance bound with a higher complexity that can be used for a theoretical performance investigation. For the Gaussian case under JML decoding, they show that the newly designed codes provide significant improvements over point-to-point (P2P) trellis-based codes and off-the-shelf low density parity check codes. They also demonstrate that, for the case of independent and identically distributed fading, the best codes obtained by performing code search are P2P optimal ones, which is also verified by simulation results.

Unveiling the molecular structure of ethylene/1-octene multi-block copolymers from chain shuttling technology

A method for assessing the puzzling molecular architecture of ethylene/1-octene multi-block copolymers, synthesized via chain-shuttling technology, is proposed. They are commercial elastomers characterized by alternating segments with low (hard blocks) and high (soft blocks) octene concentration. Our molecular assessment allows determining plausible value for the average length of blocks and number of blocks/chain, setting the basis for a definitive elucidation of structure-properties relationships of these elusive systems. Namely, the molecular basis which explains the similar crystallization properties, and the large difference in mechanical properties of this class of copolymers is unveiled thanks to our approach. We demonstrate that at 25 °C we have similar values of Young modulus and deformation at break higher than 1400%, but large strain hardening before breaking or flat mechanical behavior up to the break, depending on the short or long average block length of the multiblock copolymers, respectively, coupled with a high or low number of blocks/chain, respectively. At 60 °C these differences are amplified entailing no strain hardening but preservation of high ductility for copolymers with short average block length and high number of blocks/chain, remarkable decrease of strain at break of about two orders of magnitude (from ≈2000 to ≈90%) for copolymers with long average block length and lower number of blocks/chain.

Neyman–Pearson Test for Zero-Rate Multiterminal Hypothesis Testing

The problem of zero-rate multiterminal hypothesis testing is revisited from the perspective of information-spectrum approach and finite blocklength analysis. A Neyman–Pearson-like test is proposed and its non-asymptotic performance is clarified, for a short block length, it is numerically determined that the proposed test is superior to the previously reported Hoeffding-like test proposed by Han–Kobayashi. For a large deviation regime, it is shown that our proposed test achieves an optimal trade-off between the type I and type II exponents presented by Han–Kobayashi. Among the class of symmetric (type-based) testing schemes, when the type I error probability is non-vanishing, the proposed test is optimal up to the second-order term of the type II error exponent; the latter term is characterized in terms of the variance of the projected relative entropy density. The information geometry method plays an important role in the analysis as well as the construction of the test.

The effects of the rotational speed of voussoir beam structures formed by key strata on the ground pressure of stopes

Underground coal mining leads to fracture and movement in the overburden and the occurrence of weighting events in stopes. There are certain key strata that play an important role in controlling overburden movements. After the key stratum breaking, the fractured blocks would form the voussoir beam structure. The rotational speed of the voussoir beam structures directly affects the intensity of the ground pressures in a stope. In this study, a mechanical model was constructed to describe the rotational motions of the voussoir beam structures formed by the key strata based on elastomechanical theories. The angular velocity equations for the rotational motions of the voussoir beam structures in the key strata were obtained. Moreover, the manner in which loads and block lengths affect the angular velocity was investigated. The rotational angular velocity of the fractured blocks was found to increase with greater overlying loads on the key strata and shorter block lengths. The main roof has a major influence on strata behavior in stopes, and increases in the angular velocity of its voussoir beam structures increase roof subsidence rates, the yield of powered supports within each coal mining cycle, and the intensity of weighting events in stopes. If one or more of the voussoir beam structures formed by key strata above the main roof have greater rotational speeds than those of their underlying key strata, additional loads are applied to the latter, causing their rotational speeds to increase. If this application of loads is transmitted to the main roof, there is a strong possibility that highly intense weighting events will occur as a result of increases in the rotational speed of the main roof's voussoir beam structures. The research result provided a rational explanation for the significant differences in the weighting events of the No. 52304 working face in the Daliuta Coal Mine, which was covered by thick versus thin Aeolian sands. The results may be greatly significant in evaluating the intensity of weighting events, predicting the scope in which the strata movement affects the weighting events in stopes and determining a reasonable powered support capacity.

Iterative Detection and Decoding for Large-Scale Multiple-Antenna Systems With 1-Bit ADCs

We present a novel iterative detection and decoding scheme for uplink large-scale multiuser multiple-antenna systems. In order to reduce the receiver’s energy consumption and computational complexity, 1-bit analog-to-digital converters are used in the front-end. The performance loss due to the 1-bit quantization can be mitigated by using large-scale antenna arrays. We propose a linear low-resolution-aware minimum mean square error detector for soft multiuser interference mitigation. Moreover, short block length low-density parity-check codes are considered for avoiding high latency. In the channel decoder, a quasi-uniform quantizer with scaling factors is devised to lower the error floor of low-density parity-check codes. Simulations show good performance of the system in terms of bit error rate as compared to prior work.

Joint source and channel coding with systematic polar codes for wireless sensor communication in next generation networks

Polar codes have strongly entered into action within the standardization of the next generation 5G mobile communication systems, which are expected to be an enabling technology for the Internet of Things where networks with a large number of sensors have to handle massive connectivity demands. This paper proposes and investigates the use of systematic polar codes for joint source-channel coding of correlated sources in wireless sensor networks, thus allowing the compression of the volume of data to be transmitted over the network on one hand, and on the other hand, the protection of this data from channel impairments. Results show that systematic polar codes can achieve a distributed compression with rates close to theoretical limits, with better error rates obtained for larger blocks, and a better robustness against transmission errors obtained with stronger compression and shorter block lengths. Furthermore, while the system is able to overcome the effect of noise on parity information with adequate power management, noisy side information significantly degrades system performance with remarkable gaps towards the case of distributed compression with an ideal transmission channel.