Finite-length Codes Research Articles

Finite-Blocklength Analysis of Coded Modulation with Retransmission.

The rapid developments of 5G and B5G networks have posed higher demands on retransmission in certain scenarios. This article reviews classical finite-length coding performance prediction formulas and proposes rate prediction formulas for coded modulation retransmission scenarios. Specifically, we demonstrate that a recently proposed model for correcting these prediction formulas also exhibits high accuracy in coded modulation retransmissions. To enhance the generality of this model, we introduce a range variable Pfinal to unify the predictions with different SNRs. Finally, based on simulation results, the article puts forth recommendations specific to retransmission with a high spectral efficiency.

Cross-Layer Optimization for Statistical QoS Provision in C-RAN With Finite-Length Coding

Cross-Layer Optimization for Statistical QoS Provision in C-RAN With Finite-Length Coding

Performance Analysis of RIS-Assisted Coded Cooperation System Based on Polar Codes with Finite Code Length

Performance Analysis of RIS-Assisted Coded Cooperation System Based on Polar Codes with Finite Code Length

Implementation of scheduling in hybrid power domain non‐orthogonal multiple access system considering adaptive modulation and coding schemes selection

SummaryCommunication systems that simultaneously combine orthogonal (OMA) and nonorthogonal multiple access (NOMA) are currently under research. Such systems are called hybrid and have more flexibility in user multiplexing, which allows for increased system capacity. One of the main focus areas of research in such systems is radio resource scheduling. The existing research works on scheduling approaches are based on the Shannon's formula, which can be used to obtain the limit capacity by ideal modulation and coding schemes (MCS). However, it is more correct to consider scheduling based on the real capacity. To get it, one should consider the performance of real MCSs with finite code length; however, they are very rarely taken into account in NOMA research. The reason is that one of the basic unresolved problems in NOMA is MCS selection for users. To solve it, we have presented a table of joint pairwise MCS combinations with their adaptive selection for NOMA. In this work, we propose a radio resource scheduling approach for the OMA/NOMA system based on real MCSs that uses our own method of joint MCS selection for two NOMA users. By performing the simulation of the proposed scheduling approach, we have obtained both total and user capacity in the OMA/NOMA system, as well as the distribution of traffic among users, demonstrating the execution of the scheduling strategies.

ORBGRAND Is Almost Capacity-Achieving

Decoding via sequentially guessing the error pattern in a received noisy sequence has received attention recently, and ORBGRAND has been proposed as one such decoding algorithm that is capable of utilizing the soft information embedded in the received noisy sequence. An information theoretic study is conducted for ORBGRAND, and it is shown that the achievable rate of ORBGRAND using independent and identically distributed random codebooks almost coincides with the channel capacity, for an additive white Gaussian noise channel under antipodal input. For finite-length codes, improved guessing schemes motivated by the information theoretic study are proposed that attain lower error rates than ORBGRAND, especially in the high signal-to-noise ratio regime.

IC-LDPC Polar codes-based reconciliation for continuous-variable quantum key distribution at low signal-to-noise ratio

The error correction of information reconciliation affects the performance of the continuous-variable quantum key distribution (CV-QKD). Polar codes can be strictly proven to reach the Shannon-limit. However, due to the insufficient polarization of finite code-length, partial subchannels are neither completely noise-free nor completely noisy. In this paper, an intermediate channel low-density parity check code concatenated polar code (IC-LDPC Polar codes)-based reconciliation for CV-QKD is proposed for the above shortcomings. The experimental results show that the reconciliation efficiency of IC-LDPC Polar code can be over 98% when the signal-to-noise ratio is from −13.2 dB to −20.8 dB, the secret keys can be extracted, and the minimum frame error rate (FER) is 0.19. Therefore, the proposed scheme can improve the reconciliation efficiency and reduce the FER at a very low signal-to-noise ratio range, and it is more useful for a practical long-distance CV-QKD system.

A golden decade of polar codes: From basic principle to 5G applications

After the pursuit of seventy years, the invention of polar codes indicates that we have found the first capacity-achieving coding with low complexity construction and decoding, which is the great breakthrough of the coding theory in the past two decades. In this survey, we retrospect the history of polar codes and summarize the advancement in the past ten years. First, the primary principle of channel polarization is investigated such that the basic construction, coding method and the classic successive cancellation (SC) decoding are reviewed. Second, in order to improve the performance of the finite code length, we introduce the guiding principle and conclude five design criteria for the construction, design and implementation of the polar code in the practical communication system based on the exemplar schemes in the literature. Especially, we explain the design principle behind the concatenated coding and rate matching of polar codes in 5G wireless system. Furthermore, the improved SC decoding algorithms, such as SC list (SCL) decoding and SC stack (SCS) decoding etc., are investigated and compared. Finally, the research prospects of polar codes for the future 6G communication system are explored, including the optimization of short polar codes, coding construction in fading channels, polar coded modulation and HARQ, and the polar coded transmission, namely polar processing. Predictably, as a new coding methodology, polar codes will shine a light on communication theory and unveil a revolution in transmission technology.

Concatenated turbo polar-convolutional codes based on soft cancellation algorithm

This paper presents the Parallel and Serial Concatenated Turbo Polar-Convolutional Codes (CTPCCs) to improve the performance of polar codes in the finite code length regime. Both proposed concatenated codes use the Systematic Polar Code (SPC) and Recursive Systematic Convolutional (RSC) code as constituent codes. The iterative decoding algorithms of the proposed systems consist of a Soft Cancellation (SCAN) decoder with a single internal iteration for the SPC and SOVA or LogMap decoder for the RSC code. The simulation results show that the performance of the Parallel Concatenated Turbo Polar-Convolutional Code (PCTPCC) at low signal-to-noise ratios (SNRs) is better than that of the Serial Concatenated Turbo Polar-Convolutional Code (SCTPCC) and also better than the performance of other Turbo Polar Codes (TPCs). At BER=10−2, the proposed PCTPCC with SOVA and LogMap algorithms has about 0.3 dB and 0.25 dB performance gains over the SCTPCC models, respectively. In the high SNR regions, the performance of the SCTPCC with the LogMap algorithm significantly outperforms that of other models. At BER=10−6, the proposed SCTPCC models with SOVA and LogMap algorithms outperform the PCTPCC model by gains of 0.3 dB and 0.25 dB, respectively. The PCTPCC model with the SOVA decoder is superior to other models in terms of complexity.

Modulated Sparse Superposition Codes for the Complex AWGN Channel

This paper studies a generalization of sparse superposition codes (SPARCs) for communication over the complex additive white Gaussian noise (AWGN) channel. In a SPARC, the codebook is defined in terms of a design matrix, and each codeword is a generated by multiplying the design matrix with a sparse message vector. In the standard SPARC construction, information is encoded in the locations of the non-zero entries of the message vector. In this paper we generalize the construction and consider modulated SPARCs, where information in encoded in both the locations and the values of the non-zero entries of the message vector. We focus on the case where the non-zero entries take values from a phase-shift keying (PSK) constellation. We propose a computationally efficient approximate message passing (AMP) decoder, and obtain analytical bounds on the state evolution parameters which predict the error performance of the decoder. Using these bounds we show that PSK-modulated SPARCs are asymptotically capacity achieving for the complex AWGN channel, with either spatial coupling or power allocation. We also provide numerical simulation results to demonstrate the error performance at finite code lengths. These results show that introducing modulation to the SPARC design can significantly reduce decoding complexity without sacrificing error performance.

Control-Aware Energy-Efficient Transmissions for Wireless Control Systems With Short Packets

In this article, we investigate control-aware energy-efficient transmission strategies for wireless control systems with short packets (WCSs), in which remote state estimation error, system stability, transmission energy consumption, and communication packets with finite-length coding are all taken into account. Specifically, we formulate the transmission strategy design problem as a multiobjective optimization problem, which minimizes the remote state estimation error and transmission energy consumption simultaneously under the constraints of system stability and short packet communications. To solve the multiobjective optimization problem, we first introduce a novel objective function that encapsulates two different objective functions into a single one by using weight parameters, and further prove that the solution of the new stochastic optimization problem is a nondominated solution of the original one. Moreover, to solve the new stochastic optimization, we propose a dynamic control-aware energy-efficient transmission (DCET) algorithm that pushes the objective cost close to the optimal with a tradeoff in virtual queue backlogs for constraints. In particular, to tackle the nonconvexity constraint due to short packet communications, we introduce an additional constraint, with which the optimization problem is convex. Finally, simulation results verified the superiority of our proposed transmission strategy as compared with schemes of TDMA and Aloha-RAM multi access.

Learning end-to-end codes for the BPSK-constrained Gaussian wiretap channel

Finite-length codes are learned for the Gaussian wiretap channel in an end-to-end manner assuming that the communication parties are equipped with deep neural networks (DNNs), and communicate through binary phase-shift keying (BPSK) modulation scheme. The goal is to find codes via DNNs which allow a pair of transmitter and receiver to communicate reliably and securely in the presence of an adversary aiming at decoding the secret messages. Following the information-theoretic secrecy principles, the security is evaluated in terms of mutual information utilizing a deep learning tool called MINE (mutual information neural estimation). System performance is evaluated for different DNN architectures, designed based on the existing secure coding schemes, at the transmitter. Numerical results demonstrate that the legitimate parties can indeed establish a secure transmission in this setting as the learned codes achieve points on almost the boundary of the equivocation region.

Input-Distribution-Aware Successive Cancellation List Decoding of Polar Codes

Polar codes are linear block codes that can achieve channel capacity at infinite code length. Successive cancellation list (SCL) decoding relies on a set of parallel decoders; it yields good error-correction performance at finite code length, at the cost of increased implementation complexity and power consumption. Current efforts in literature focus on design-time decoder complexity reduction, while lacking practical run-time power reduction methods. In this work, input-distribution-aware SCL (IDA-SCL) decoding is proposed, that allows to determine the parallelism to adopt by performing simple observations on the input of the decoder. This technique guarantees fixed, short latency and allows hardware SCL decoders to dynamically shut down part of the internal parallelism before each decoding process. It can be combined with existing complexity- and power- reduction techniques. Simulation results show that IDA-SCL can reduce the run-time complexity of SCL of up to 50%.

On the Achievable Rate Under Finite Codelength for RIS-Aided Systems

The ideal Shannon channel capacity can only be achieved by infinite codelength, so it is not accurate for practical finite codelength. The codelength of channel coding schemes heavily affects the performance of communication systems, but it cannot be too long to ensure affordable decoding complexity and latency. Unfortunately, existing performance analysis for systems aided by reconfigurable intelligent surface (RIS) only focus on the ideal channel capacity and neglect the achievable rate loss caused by finite codelength. To fill in this gap, this paper analyzes the achievable rate under finite codelength in a time-coherent RIS-aided systems, and gives an approximate analytic solution based on Taylor expansion and multi-dimensional central limit theorem. To be more specific, the closed form approximated achievable rate is given based on Taylor expansion, and it is shown that the required codelength decreases superlinearly with the increase of the number of RIS elements. Simulation results verify the analysis, and demonstrate the advantage of RIS-aided systems over the traditional large antenna array schemes.

Performance analysis of the bioinspired method for optimizing irregular codes with a low density of parity checks

This paper reports the principles of building irregular codes with a low density of parity checks. It has been determined that finding irregular finite-length codes with improved characteristics necessitates the optimization of the distributions of powers of the symbol and test vertices of the corresponding Tanner graph. The optimization problem has been stated and the application of a bioinspired approach to solving it has been substantiated. The paper considers the main stages of the bioinspired method to optimize the finite-length irregular codes with a low density of parity checks. It is shown that a given method is based on the combined application of the bioinspired procedure of bats, a special method for building Tanner graphs, and computer simulation. The reported study aimed to evaluate the effectiveness of the proposed method for optimizing irregular codes when using the selected bioinspired procedure and the predefined model of a communication channel. Based on the study results, it has been determined that the optimized relatively short irregular codes with a low density of parity checks possess better characteristics compared to existing codes. It is shown that the derived codes do not demonstrate the effect of an floor and ensure an energy win via encoding of about 0.5 dB compared to regular codes depending on the length of the code. It has been determined that the optimization of irregular codes with a low value of the maximum power in the distribution of powers of the symbol vertices of the Tanner graph leads to a decrease in the order of an error coefficient in the region with a high signal/noise ratio. The application of the optimized irregular codes with a low density of parity checks could improve the efficiency of next-generation wireless telecommunication systems

On the optimization of resources for short frame synchronization

We consider the transmissions of successive short packets. Each of them combines information to be transmitted (codeword) with information for synchronizing the frame (syncword). For short packets, the cost of including syncwords is no longer negligible and its design requires careful optimization. In particular, a trade-off arises depending on the way the total transmit power or the total frame length is split among the syncword and the codeword. Assuming optimal finite-length codes, we develop tight upper bounds on the probability of erroneous synchronization, for both frames with concatenated syncword and frames with superimposed syncword. We use these bounds to optimize this trade-off. Simulation results show that the proposed bounds and analysis have practical relevance for short packet communication system design.

Repetition-Based NOMA Transmission and Its Outage Probability Analysis

In this paper, we discuss a non-orthogonal multiple access (NOMA) scheme to exploit a high diversity gain using repetition, namely repetition-based NOMA. Unlike conventional power-domain NOMA, all the users can have the same transmit power, but different number of repetitions. Thanks to a high diversity gain, a low outage probability can be achieved without instantaneous channel state information (CSI) feedback for power allocation. A closed-form expression for an upper-bound on the outage probability is derived so that the values of key parameters can be decided to maintain the outage probability below a target value. We also consider the average error probability for finite-length codes. Simulation results are compared with the derived bounds and it is shown that the bounds are reasonably tight and can be used to decide key parameters (e.g., code rates) to guarantee target error probabilities.

Computing Algorithms for LDPC Coded Internet-of-Things

Low-density parity-check (LDPC) codes are widely employed in communication systems. We focus on the computing of messages at the sink node of internet-of-things (IoT). As opposed to decoding all the messages, we consider the case that the sink node is interested in computing a linear transformation of the messages. We assume that all the IoT devices are identical. We first present three representations of the considered systems, based on which three multistage computing algorithms are proposed, which are decoding-computing (DC) algorithm, computing-decoding (CD) algorithm, and computing-decoding-computing (CDC) algorithm. Secondly, we show that the considered system admits a compact normal graph representation, based on which a joint computing algorithm is proposed. Thirdly, we present numerical results to show the advantages of the proposed algorithms. Numerical results show that the optimality of the proposed algorithms depends on the channel conditions and the computing functions. Numerical results also show that the joint computing algorithm has the best performances for a variety of scenarios. Finally, we present a simulation-based optimization procedure to design finite-length LDPC codes for the joint computing algorithm.

Resource allocation for secure Gaussian parallel relay channels with finite-length coding and discrete constellations

We investigate the transmission of a secret message from Alice to Bob in the presence of an eavesdropper (Eve) and many of decode-and-forward relay nodes. Each link comprises a set of parallel channels, modeling for example an orthogonal frequency division multiplexing transmission. We consider the impact of efficient implementations, including discrete constellations and finite-length coding, defining an achievable secrecy rate under a constraint on the equivocation rate at Eve. Then, we propose a power and channel allocation algorithm that maximizes the achievable secrecy rate by resorting to two coupled Gale-Shapley algorithms for stable matching problem. We consider the scenarios of both full and partial channel state information at Alice. In the latter case, we only guarantee an outage secrecy rate, i.e., the rate of a message that remains secret with a given probability. Numerical results are provided for Rayleigh fading channels in terms of average outage secrecy rate, showing that practical schemes achieve a performance quite close to that of ideal ones.

End-to-End Performance Analysis of Delay-Sensitive Multi-Relay Networks

We study the end-to-end (E2E) performance of multi-relay networks in delay-constrained applications. The results are presented for both decode-and-forward (DF) and AF (A: amplify) relaying schemes. We use some fundamental results on the achievable rates of finite-length codes to analyze the system performance in the cases with short packets. Taking the message decoding delays and different numbers of hops into account, we derive closed-form expressions for the E2E packet transmission delay, the E2E error probability as well as the E2E throughput. Moreover, for different message decoding delays, we determine the appropriate codeword length and the relay power such that the same E2E error probability and packet transmission delay are achieved in the AF- and DF-relay networks. As we show, for different codeword lengths and numbers of hops, the E2E performance of multi-relay networks are affected by the message decoding delay of the nodes considerably.

Finite-length performance comparison of network codes using random vs Pascal matrices

In this letter, we evaluate the finite-length performance of network coding when using either random or structured encoding matrices. First, we present our novel construction of structured network codes over Fq(q=2m) using Pascal matrices. We present their encoding, re-encoding and decoding in matrix notation and derive their packet loss rate. Second, we propose a novel methodology to compute the optimal finite-length coding rate for representative and realistic traffic applications. Finally, our method allows to compare the performance of our codes with the performance of popular random codes. We show that our constructions always have better throughput and minimal overhead, which is more significant for short code lengths. Further, their larger decoding delay fulfils the delay constraints of realistic scenarios (e.g. 5G multihop networks).