Codeword Length Research Articles

Consensus for Heterogeneous Multiagent Systems: Output Rate-Coded Secure Control.

This article investigates an output rate-coded secure control based on backstepping for the consensus of heterogeneous multiagent systems (MASs) with output-triggering condition. Due to the nondifferentiable virtual control inputs caused by discontinuous triggering signals, it presents a technical obstacle in implementing the recursive backstepping, rendering previous results inapplicable. To address this problem, an auxiliary high-order filter is elaborately constructed to guarantee the required-order derivatives of virtual control inputs. As this filter is driven by local triggering consensus error, it allows our MASs to have different system orders and relative degrees. Besides, to reduce communication bit and strengthen communication security, we propose a novel distributed rate-coded algorithm from an encoding-decoding viewpoint. When it is triggered, agent's output is encrypted into an L -length codeword, then transmitted to neighbors without exposing any sensitive system states or real control inputs. It is shown that all the closed-loop system signals are ultimately bounded, and the mean square consensus tracking error can be reduced by appropriately selecting control parameters. Simulations illustrate our theoretical finding.

Adaptive Segmented Aggregation and Rate Assignment Techniques for Flexible-Length Polar Codes.

Polar codes have garnered a lot of attention from the scientific community, owing to their low-complexity implementation and provable capacity achieving capability. They have been standardized to be used for encoding information on the control channels in 5G wireless networks due to their robustness for short codeword lengths. The conventional approach to generate polar codes is to recursively use 2×2 kernels and polarize channel capacities. This approach however, has a limitation of only having the ability to generate codewords of length Norig=2n form. In order to mitigate this limitation, multiple techniques have been developed, e.g., polarization kernels of larger sizes, multi-kernel polar codes, and downsizing techniques like puncturing or shortening. However, the availability of so many design options and parameters, in turn makes the choice of design parameters quite challenging. In this paper, the authors propose a novel polar code construction technique called Adaptive Segmented Aggregation which generates polar codewords of any arbitrary codeword length. This approach involves dividing the entire codeword into smaller segments that can be independently encoded and decoded, thereby aggregated for channel processing. Additionally a rate assignment methodology has been derived for the proposed technique, that is tuned to the design requirement.

PCC Polar Codes for Future Wireless Communications: Potential Applications and Design Guidelines

The main limitation of polar codes is that the channel polarization is insufficient in the context of short and moderate codeword length, resulting in a degradation of error correction performance. Promising solutions can be found in the recently proposed parity-check-concatenated (PCC) polar codes, which exploit the scattered parity bits to improve the error correction capability substantially. Owing to this benefit, PCC polar codes constitute an appealing paradigm of channel coding and have been deemed a critical technology of the control channel coding for 5G mobile communication. As an emerging channel coding, its potentiality has yet to be thoroughly investigated. To unleash the eminent benefits of the PCC polar codes, in this article, we present a comprehensive overview, including its innovative construction of encoding, low-complexity decoding, advanced evolution variants, and potential application scenarios, as well as its future design guidelines.

Deterministic K-Identification for Future Communication Networks: The Binary Symmetric Channel Results

Numerous applications of the Internet of Things (IoT) feature an event recognition behavior where the established Shannon capacity is not authorized to be the central performance measure. Instead, the identification capacity for such systems is considered to be an alternative metric, and has been developed in the literature. In this paper, we develop deterministic K-identification (DKI) for the binary symmetric channel (BSC) with and without a Hamming weight constraint imposed on the codewords. This channel may be of use for IoT in the context of smart system technologies, where sophisticated communication models can be reduced to a BSC for the aim of studying basic information theoretical properties. We derive inner and outer bounds on the DKI capacity of the BSC when the size of the goal message set K may grow in the codeword length n. As a major observation, we find that, for deterministic encoding, assuming that K grows exponentially in n, i.e., K=2nκ, where κ is the identification goal rate, then the number of messages that can be accurately identified grows exponentially in n, i.e., 2nR, where R is the DKI coding rate. Furthermore, the established inner and outer bound regions reflects impact of the input constraint (Hamming weight) and the channel statistics, i.e., the cross-over probability.

An improved algorithm of generating shortening patterns for polar codes

The rate matching in polar codes becomes a solution when non-conventional codewords of length N≠2n are required. Shortening is employed to design arbitrary rate codes from a mother code with a given rate. Based on the conventional shortening scheme, length of constructed polar codes is limited. In this paper, we demonstrate the presence of favorable and unfavorable shortening patterns. The structure of polar codes is leveraged to eliminate unfavorable shortening patterns, thereby reducing the search space. We generate an auxiliary matrix through likelihood and subsequently select the shortening bits from the matrix. Unlike different existing methods that offer only a single shortening pattern, our algorithm generates multiple favorable shortening patterns, encompassing all possible favorable configurations. This algorithm has a reduced complexity and suboptimal performance, effectively identifying shortening patterns and sets of frozen symbols for any polar code. Simulation results underscore that the shortened polar codes exhibit performance closely aligned with the mother codes. Our algorithm addresses this security concern by making it more difficult for an attacker to obtain the information set and frozen symbols of a polar code. This is done by generating multiple shortening patterns for any polar code.

In search of maximum non-overlapping codes

AbstractNon-overlapping codes are block codes that have arisen in diverse contexts of computer science and biology. Applications typically require finding non-overlapping codes with large cardinalities, but the maximum size of non-overlapping codes has been determined only for cases where the codeword length divides the size of the alphabet, and for codes with codewords of length two or three. For all other alphabet sizes and codeword lengths no computationally feasible way to identify non-overlapping codes that attain the maximum size has been found to date. Herein we characterize maximal non-overlapping codes. We formulate the maximum non-overlapping code problem as an integer optimization problem and determine necessary conditions for optimality of a non-overlapping code. Moreover, we solve several instances of the optimization problem to show that the hitherto known constructions do not generate the optimal codes for many alphabet sizes and codeword lengths. We also evaluate the number of distinct maximum non-overlapping codes.

Novel Generalized Entropy Measure's Characteristics Associated with Code-Word Length

In this article, we introduce a novel, all-purpose entropy measure and derive a new, all-purpose average codeword length in accordance with it. After that, we determined new average generalized codeword length constraints in terms of additional metrics of generalized entropy. In addition, we demonstrate that the metrics employed in this study are generalizations of other metrics typically employed in the coding and information theory communities.

Finite Blocklength Regime Performance of Downlink Large Scale Networks

Some emerging 5G and beyond use-cases impose stringent latency constraints, which necessitates a paradigm shift towards finite blocklength performance analysis. In contrast to Shannon capacity-achieving codes, the codeword length in the finite blocklength regime (FBR) is a critical design parameter that imposes an intricate tradeoff between delay, reliability, and information coding rate. In this context, this paper presents a novel mathematical analysis to characterize the performance of large-scale downlink networks using short codewords. Theoretical achievable rates, outage probability, and reliability expressions are derived using the finite blocklength coding theory in conjunction with stochastic geometry, and compared to the performance in the asymptotic regime (AR). Achievable rates under practical modulation schemes as well as multilevel polar coded modulation (MLPCM) are investigated. Numerical results provide theoretical performance benchmarks, highlight the potential of MLPCM in achieving close to optimal performance with short codewords, and confirm the discrepancy between the performance in the FBR and that predicted by analysis in the AR. Finally, the meta distribution of the coding rate is derived, providing the percentiles of users that achieve a predefined target rate in a network.

AN IMPROVED POLARIZATION WEIGHTS CONSTRUCTION FOR POLAR CODES

Polar codes proposed by Arikan based on channel polarization have been proven to achieve Symmetric Binary-Discrete Input Memoryless Channels capacity. 3GPP has also chosen the Polar codes as the error correction code in the fifth mobile communication system (5G New Radio - 5G NR) with a maximum codeword length of 1024 bits. The design of the code based on the reliability of the synthetic channels has been researched with many different methods to satisfy the requirements demanded in the application of 5G NR. The Polar codes design requirements are ease of implementation, low decoding complexity, and high performance in error correction. This paper has proposed a method of designing Polar codes by determining a synthetic channels reliability index sequence based on the Polarization Weights (PW) method called the Improved Polarization Weights (IPW) method. The simulation results show that the error correction performance of the code designed according to IPW is better than the code structure selected for 5G NR and designed according to the original PW method.

An optimal channel coding scheme for high-speed data communication

This paper presents a novel channel-coding scheme called Binary to Gray Code Conversion based Error Detection and Correction (BGCC-EDAC) code to correct the maximum number of errors that occur at the receiving end during wireless transmission. The proposed method adds the parity bit using Binary to Gray Code Conversion (BGCC). The decoding algorithm proposed in this paper will not perform the regular Gray-to-Binary code conversion. Instead, a novel decoding algorithm is proposed to detect and correct most of the errors in the message bits. It will require retransmission only if any parity error occurs. The efficiency of the proposed channel code stems from its redundant bit calculation and decoding algorithm. The simulation results using Cadence 90 nm technology show that the proposed BGCC-EDAC code consumes low power, less area, and less propagation delay. Simulation analysis using MATLAB reveals that the proposed BGCC-EDAC outperforms the existing error-correcting codes in terms of BER performance. This makes the proposed BGCC-EDAC code, with a shorter code word length, highly suitable for high-speed, reliable data communications.

Bandwidth Density Analysis of Coded Free-Space Optical Interconnects

The performance of free-space optical interconnects (FSOIs) system is significantly influenced by noise, similar to any wireless communication system. This noise has a notable impact on both the bandwidth density and data rate of FSOIs system. To address these challenges, this study proposes the utilization of vertical-cavity-surface-emitting laser (VCSEL) arrays on the transmitter side and photodetector arrays on the receiver side for FSOIs. The study investigates the bandwidth density of the system with and without coding while maintaining a specific bit error rate. An analysis is conducted in the presence of higher-order modes in the laser beams of the FSOIs system and a fundamental Gaussian operating mode. The presence of the higher-order modes leads to degradation in the performance of the FSOIs system in terms of bandwidth density. In addition, we examine the impact of the signal-to-noise ratio (SNR) on the system’s bandwidth density for each considered operating mode. The provided simulation results clearly demonstrate that coding significantly enhances the bandwidth density of the systems, with the extent of improvement being closely tied to the employed code rate and codeword length.

Design and implementation of virtual-single-length turbo decoder for multi-user parallel decoding

Dealing with multiple users in cellular basestation with multiple codewords of variable length is a challenging task in parallel decoding. Thus, a novel turbo decoder with variable codeword-based parallel decoding is proposed for the 3GPP LTE (4G) system. To make multi-user decoding more efficient, all users are aggregated into a single block with zero insertions where all users can be decoded in the same cycle. Different users are separated by additional zeros to decode in parallel and improve the hardware utilization. Moreover, a stationary boundary enhancement is utilized to exchange and update the decoded messages between different sub-blocks of codeword for the next decoding interaction. This scheme can balance the performance loss and decoding latency of variable codeword-based parallel decoding. The proposed turbo decoder has a maximum throughput of 280.5 Mbps (VC707) and 212 Mbps (ZC706), where the design has been integrated and tested with OpenAirInterface (OAI) 4G eNB in campus trials.

Rate-Diverse Multiple Access Over Gaussian Channels

In this work, we develop a pair of rate-diverse encoder and decoder for a two-user Gaussian multiple access channel (GMAC). The proposed scheme enables the users to transmit with the same codeword length but different coding rates under diverse user channel conditions. First, we propose the row-combining (RC) method and row-extending (RE) method to design practical low-density parity-check (LDPC) channel codes for rate-diverse GMAC. Second, we develop an iterative rate-diverse joint user messages decoding (RDJD) algorithm for GMAC, where all user messages are decoded with a single parity-check matrix. In contrast to the conventional network-coded multiple access (NCMA) and compute-forward multiple access (CFMA) schemes that first recover a linear combination of the transmitted codewords and then decode both user messages, this work can decode both the user messages simultaneously. Extrinsic information transfer (EXIT) chart analysis and simulation results indicate that RDJD can achieve gains up to 1.0 dB over NCMA and CFMA in the two-user GMAC. In particular, we show that there exists an optimal rate allocation for the two users to achieve the best decoding performance given the channel conditions and sum rate.

Towards the Designing of Low-Latency SAGIN: Ground-to-UAV Communications over Interference Channel

We present a novel and first-of-its-kind information-theoretic framework for the key design consideration and implementation of a ground-to-unmanned Aerial Vehicle (UAV) (G2U) communication network with an aim to minimize end-to-end transmission delay in the presence of interference in Space-Air-Ground Integrated Networks (SAGIN). To characterize the transmission delay, we utilize Fano’s inequality and derive the tight upper bound for the capacity for the G2U uplink channel in the presence of interference, noise, and potential jamming. In addition, as a function of the location information of the UAV, a tight lower bound on the transmit power is obtained subject to the reliability constraint and the maximum delay threshold. Furthermore, a relay UAV in the dual-hop relay mode, with amplify-and-forward (AF) protocol, is considered, for which we jointly obtain the optimal positions of the relay and the receiver UAVs in the presence of interference, with straight-line, circular, and helical trajectories as UAV tracing. Interestingly, increasing the power gives a negligible gain in terms of delay minimization, though may greatly enhance the outage performance. Moreover, we prove that there exists an optimal height that minimizes the end-to-end transmission delay in the presence of interference. We show the interesting result of the delay analysis. In particular, it is shown that receiver location and the end-to-end signal-to-noise power ratio play a critical role in end-to-end latency. For instance, with the transmitter location fixed to (0, 0, 0) and the interferer location set to (0, 500 m, 0), the latency generally increases with increasing the receiver’s vertical height (z-axis). With the receiver’s horizontal coordinates, i.e., (xR, yR) set to (0, 0) reducing the receiver’s height from 200 m to 50 m decreases the delay latency (codeword length) by more than 30% for an interference-limited channel. Whereas, for an interference channel with a signal-to-noise power ratio equal to 30 dB, the latency decreases by approximately 2%. The proposed framework can be used in practice by a network controller as a system parameters selection criteria, where among a set of parameters, the parameters leading to the lowest transmission latency can be incorporated into the transmission. The based analysis further set the baseline assessment when applying Command and Control (C2) standards to mission-critical G2U and UAV-to-UAV (U2U) services.

Secret key rate of continuous-variable quantum key distribution with finite codeword length

Secret key rate of continuous-variable quantum key distribution with finite codeword length

A Segmented-Edit Error-Correcting Code With Re-Synchronization Function for DNA-Based Storage Systems

As a powerful tool for storing digital information in chemically synthesized molecules, DNA-based data storage has undergone continuous development and received increasingly more attention. Efficiently recovering information from large-scale DNA strands that suffer from insertions, deletions, and substitution errors (collectively referred to as edit errors), is one of the major bottlenecks in DNA-based storage systems. To cope with this challenge, in this paper, we provide a segmented-edit error-correcting code with the re-synchronization function, termed the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">DNA-LM</i> code. Compared with the previous segmented-error-correcting codes, it has a systematic structure and does not require the endpoint of the received segment as pre-requisite information for decoding. In the case that the number of edit errors exceeds the edit error-correcting capability of a segment, it can easily regain synchronization to ensure that the subsequent decoding continues. Both encoding and decoding complexity is linear in the codeword length. The redundancy of each segment is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\lceil \log k\rceil +6$</tex-math></inline-formula> quaternary symbols, where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$k$</tex-math></inline-formula> is the length of the message segment. We further generalize the decoding algorithm to deal with duplicated DNA strands, whereas it still maintains linear time complexity in the codeword length and the number of duplications. Simulations under a stochastic edit errors model show that, at a low raw error rate of the “next-gen” sequencing, our code can enable error-free decoding by concatenating with the (255,223) RS code.

ELDPC: An Efficient LDPC Coding Scheme for Phase-Change Memory

Low read latency, long lifetime, and high storage density have all been demonstrated in phase-change memory (PCM), making it an attractive contender for main memory. However, due to resistance drift per cell caused by long-term storage, data reliability becomes a major challenge. Low-density parity-check (LDPC) codes with improved error correction capability can be used in PCM to reduce bit error rates and thus improve data reliability. More interestingly, when the raw bit error rates (RBER) of various pages in PCM is compared at the same storage time, a considerable gap appears, resulting in high sensing and decoding latency. We propose eLDPC, an efficient LDPC coding scheme for reducing sensing and decoding latency, in this paper. We start with a preliminary experiment, which reveals that there is a significant variation in resistance drifts between adjacent distributions, resulting in a large RBER gap for different pages. Then, using a submatrix of the parity-check matrix to shorten the codeword length, eLDPC is inspired to encode pages with lower RBER. The original bit sequence is separated into even bit sequence (EBS) and odd bit sequence (OBS) for pages with higher RBER. eLDPC is used to encode EBS and OBS independently. By utilizing optimized soft information, EBS and OBS are eLDPC decoded. eLDPC can significantly improve error correction capability of LDPC hard decoding, effectively eliminating soft decoding processes and lowering decoding latency. The results of simulations show that eLDPC can greatly decrease decoding iterations and time.

Distributed Goppa-Coded Generalized Spatial Modulation: Optimized Design and Performance Study

The distributed Goppa-coded generalized spatial modulation (DGC-GSM) scheme with the source, relay, and destination in cooperative communications is proposed, where the source and relay adopt different Goppa codes. Goppa codes have many advantages such as the flexible codeword length, excellent code construction, and easy encoding and decoding complexity. At the relay, we select portions of the source information bits for further encoding. For each selection, the destination constructs a channel code. To obtain the best code in the destination, we propose the optimal information bit selection algorithm at the relay to choose the source information. However, Goppa codes with a large block length will impose high complexity on the optimal algorithm. Thus, the locally optimized selection algorithm is further proposed. At the destination, the joint decoding algorithm is adopted to recover the source information. Our simulated results indicate that the two selection algorithms proposed achieve better performance than the random selection method. This is because the optimized algorithms can generate the code with a larger minimum distance at the destination. Moreover, the proposed DGC-GSM scheme outperforms the non-cooperative system. Moreover, the DGC-GSM scheme can obtain the approximate performance with the distributed Goppa-coded spatial modulation (DGC-SM) scheme but has a significantly reduced transmit antenna number.

Logarithmic time encoding and decoding of integer error control codes

AbstractOne of the most important characteristics of all error control codes (ECCs) is the complexity of the encoding/decoding algorithms. Today, there are many ECCs that can correct multiple bit errors, but at the price of high encoding/decoding complexity. Among the rare exceptions are integer ECCs (IECCs), whose serial encoding/decoding algorithms run in O(n) time, where n is the codeword length. In this article, we show that IECCs can be encoded/decoded even faster, that is, that their parallel encoding/decoding algorithms have O(log2n) time complexity.

Power and rate control in wireless communication systems with energy harvesting and rateless codes

In this paper, for a wireless communication system with energy harvesting and rateless error correction codes, the joint optimization of transmit power, modulation scheme and code rate to maximize the long-term average achievable transmission rate under the constraint of available energy is studied. The method is given first to determine the codeword length (or code rate) for a signal-to-noise ratio (SNR) under the constraint of a pre-defined decoding error probability. Then the formula of the actual transmission rate is deduced with a specific modulation and code rate, and the optimization problem to maximize the long-term average actual transmission rate is constructed under the constraints of available harvested energy and the decoding complexity of the rateless code. Since energy harvesting and channel fading are both stochastic processes, the optimization problem is difficult to solve. By using the Lyapunov optimization framework, the original long-term optimization problem is transformed into a per time slot one. Then an efficient numerical method is proposed to obtain the solution to the problem. The proposed algorithm is verified by simulation, and the results show that the proposed algorithm can achieve a higher average actual transmission rate than the comparison algorithms aiming at optimizing the channel capacity.