Showing papers on "Noisy-channel coding theorem published in 2020"
TL;DR: A novel code based channel shortening (CCS) algorithm for faster-than-Nyquist (FTN) signaling is proposed, where special convolutional codes are used to absorb the channel memory.
Abstract: A novel code based channel shortening (CCS) algorithm for faster-than-Nyquist (FTN) signaling is proposed, where special convolutional codes are used to absorb the channel memory. These convolutional codes have a special type of generator matrix that allows previous code symbols to be determined by the current code trellis state and thus been referred to as output-retainable convolutional codes (ORCCs). Different from conventional schemes, the CCS algorithm performs joint detection and decoding (JDD) based only on the code trellis by exploiting the ORCC structure. Therefore, it provides a new view for channel shortening techniques, i.e., absorbing the channel memory by using channel codes. Properties of ORCCs are discussed. Based on these properties, we derive the bit error rate (BER) bound for the CCS algorithm. According to the bound, a code search algorithm is proposed to facilitate the code design. Furthermore, two concatenated codes based on ORCCs are designed. Simulation results show that with a 16-states BCJR algorithm for JDD, the BER performance of the designed self-concatenated convolutional code incorporated with FTN signaling is only 0.75 dB away from the Shannon limit of the shaping pulse, and the required signal-to-noise ratio is below the BPSK limit of Nyquist signaling.
29 citations
TL;DR: Computer simulations of the resulting codes reveal that MLC not only provides significant advantages compared with BicM, but also outperforms several existing MLC and BICM proposals.
Abstract: Multilevel coding (MLC) is compared with bit-interleaved coded modulation (BICM) from a performance-versus-complexity standpoint. In both approaches, complexity-optimized error-reducing low-density parity-check inner codes are designed for concatenation with an outer hard-decision code, for various modulation orders. The codes are designed to achieve various points on the Pareto frontier characterizing the performance-complexity tradeoff. Computer simulations of the resulting codes reveal that MLC not only provides significant advantages compared with BICM, but also outperforms several existing MLC and BICM proposals. At 25% overhead, MLC provides a net coding gain of up to 12.8 dB with 16-QAM (1.0 dB from the constrained Shannon limit), a net coding gain of up to 13.6 dB with 64-QAM (1.2 dB from the constrained Shannon limit), and a net coding gain of up to 14 dB with 256-QAM (1.65 dB from the constrained Shannon limit), all with reasonable decoding complexity.
22 citations
TL;DR: Hardware architecture implementation on Xilinx XC7K325t field programmable gate array (FPGA) shows that the encoding throughput rate of the proposed FEC encoder core can reach 1.19 Gb/s and the overall data throughput is improved by 30.9% compared with the constant coding modulation (CCM) schemes.
Abstract: A powerful forward error correction (FEC) scheme based on the serial concatenation of Bose-Chaudhuri-Hocquenghen (BCH) and low-density parity-check (LDPC) codes has been adopted by the second generation digital video broadcast (DVB-S2) standard due to their near Shannon limit performance. This paper proposes an efficient FEC encoder core to support different DVB-S2 codes for variable coding modulation (VCM) schemes of low earth orbit (LEO) satellite-ground communications. By exploring the properties of different concatenated BCH-LDPC codes and reusing the computation units and memories, the compatibility is achieved and the utilization of hardware resources is improved. Besides, parallel computing is performed to speed up the acquisition of check bits, which allows the encoding throughput to be increased. Hardware architecture implementation on Xilinx XC7K325t field programmable gate array (FPGA) shows that the encoding throughput rate of the proposed FEC encoder core can reach 1.19 Gb/s. And the overall data throughput is improved by 30.9% compared with the constant coding modulation (CCM) schemes.
8 citations
TL;DR: This brief investigates the hardware design of a turbo-Hadamard encoder/decoder system and finds that the entire system has been implemented on an FPGA board.
Abstract: A turbo-Hadamard code (THC) is a type of low-rate channel code with capacity approaching the ultimate Shannon limit, i.e., −1.59 dB. In this brief, we investigate the hardware design of a turbo-Hadamard encoder/decoder system. The entire system has been implemented on an FPGA board. A bit error rate (BER) of 10−5 can be achieved at $E_{b}/N_{0} = 0.04$ dB with a throughput of 3.2 Gbps or at $E_{b}/N_{0} = -0.45$ dB with a throughput of 1.92 Gbps.
7 citations
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TL;DR: A Shannon-limit approached (SLA) IR scheme, which mainly contains two phases: the forward reconciliation phase and the acknowledgment reconciliation phase, which decreases the frame error rate of the SLA IR scheme.
Abstract: Information reconciliation (IR) corrects the errors in sifted keys and ensures the correctness of quantum key distribution (QKD) systems. Polar codes-based IR schemes can achieve high reconciliation efficiency, however, the incidental high frame error rate decreases the secure key rate of QKD systems. In this article, we propose a Shannon-limit approached (SLA) IR scheme, which mainly contains two phases: the forward reconciliation phase and the acknowledgment reconciliation phase. In the forward reconciliation phase, the sifted key is divided into sub-blocks and performed with the improved block checked successive cancellation list (BC-SCL) decoder of polar codes. Afterwards, only the failure corrected sub-blocks perform the additional acknowledgment reconciliation phase, which decreases the frame error rate of the SLA IR scheme. The experimental results show that the overall failure probability of SLA IR scheme is decreased to $10^{-8}$ and the efficiency is improved to 1.091 with the IR block length of 128Mb. Furthermore, the efficiency of the proposed SLA IR scheme is 1.055, approached to Shannon-limit, when quantum bit error rate is 0.02 and the input scale of 1Gb, which is hundred times larger than the state-of-art implemented polar codes-based IR schemes.
6 citations
25 May 2020
TL;DR: A novel type of ultimate-Shannon-limit-approaching codes, namely protograph-based low-density parity-check Hadamard (PLDPC-Hadamard) codes are proposed in this paper and a systematic way of analyzing such codes using Protograph EXtrinsic Information Transfer (PEXIT) charts is proposed.
Abstract: We propose a novel type of ultimate-Shannon-limit-approaching codes, namely protograph-based low-density parity-check Hadamard (PLDPC-Hadamard) codes in this paper. We also propose a systematic way of analyzing such codes using Protograph EXtrinsic Information Transfer (PEXIT) charts. Using the analytical technique we have found a code of rate about 0.05 having a theoretical threshold of -1.42dB. At a BER of $10^{-5}$, the gaps of our code to the Shannon capacity for R=0.05 and to the ultimate Shannon limit are 0.25 dB and 0.40 dB, respectively.
6 citations
01 Sep 2020
TL;DR: This research made a MIMO 2X2 simulation system on DVB-T2 technology with LDPC coding technique and Maximum Likelihood detector and the results obtained indicate that the system which is has smaller rate is the better system.
Abstract: The MIMO (Multiple Input Multiple Output) system works very well on multipath components. Some multipath components are exploited to increase bandwidth diversity and efficiency. In addition, this system also provides a significant increase in data throughput and communication coverage without expand the frequency and transmit power. Even so, this system is still vulnerable to InterSymbol Interference. Low Density Parity Check (LDPC) technique which is has the ability to correct errors near the Shannon limit (theoretical maximum error correction limit) and Maximum likelihood (ML) detection which is able to provide performance minimum bit errors are believed to be able to handle interference arising when passing through a channel.This research made a MIMO 2X2 simulation system on DVB-T2 technology with LDPC coding technique and Maximum Likelihood detector. The results obtained from running this simulation system indicate that the system which is has smaller rate is the better system. The ideal system without error correction code shows the Maximum Likelihood performance forming a waterfall curve and no more errors at 20 dB. While the system with LDPC and Maximum Likelihood is able to reaches BER (bit error rate) 10-2 at SNR (Signal to Noise Ratio) around 1 dB from the 1/2 rate system, and the 3/4 rate system reaches BER 10-2 at around 4 dB, and the 5/6 rate system reaches BER 10-2 at SNR around 6 dB.
4 citations
4 citations
TL;DR: This paper has demonstrated data reduction method using Principal Component Analysis (PCA) for fuse data at sensor level to transmit and regress the same at the receiver for improvising the channel capacity of the system.
3 citations
TL;DR: This finding indicates that the frozen bits in OPC has strong contribution to the error correction capability of the Polar codes and may not be replaced by other bits even though the bits are protected by other channel coding schemes.
Abstract: Polar codes ware mathematically proven to achieve the Shannon limit, where the error probability is reduced with the help of frozen bits Since the frozen bits are detrimental in terms of transmission efficiency, this paper investigates the importance of the frozen bits and the possibility of being replaced by other protected bits via a concatenation with other outer channel coding schemes We evaluate the impact of frozen bits to the capability of error correction of original Polar codes (OPC) and the concatenated Polar codes (CPC) in short block-length in terms of bit-error-rate (BER) performances Repetition codes are used as outer channel encoder prior to the Polar codes and are divided into two schemes, ie, (i) irregular repetition-CPC (IR-CPC) codes and (ii) regular repetition-CPC (RR-CPC) codes We evaluate BER performances using computer simulations based on Log-Likelihood Ratio (LLR) with the modulation of Binary Phase Shift Keying (BPSK) under Additive White Gaussian Noise (AWGN) and frequency-flat Rayleigh Fading channels We found that the OPC is better than the IR-CPC codes or RR-CPC codes for the same channel coding rate and block-length This finding indicates that the frozen bits in OPC has strong contribution to the error correction capability of the Polar codes and may not be replaced by other bits even though the bits are protected by other channel coding schemes
3 citations
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TL;DR: It turns out that a single-layered OSS code achieves the ultimate Shannon limit in the power-limited regime, even with the linear complexity decoder.
Abstract: This paper presents a new class of sparse superposition codes for low-rates and short-packet communications over the additive white Gaussian noise channel. The new code is orthogonal sparse superposition (OSS) code. A codeword of OSS codes is represented as a superposition of sparse sub-codewords whose support sets are mutually non-overlapping. To construct such codewords in a computationally efficient manner, a successive encoding method is presented. Harnessing the orthogonal property among sub-codewords, a simple yet near-optimal decoding method is proposed, which performs element-wise maximum a posterior decoding with successive support set cancellation. This decoder is super-fast by a linear decoding complexity in block lengths, far less than the commercially used channel decoders for modern channel codes. The upper bounds for the block error rates (BLERs) are analytically derived for few-layered OSS codes as a function of block lengths and code rates. It turns out that a single-layered OSS code achieves the ultimate Shannon limit in the power-limited regime, even with the linear complexity decoder. Via simulations, the proposed OSS codes are shown to perform better than commercially used coded modulation techniques for low-rate and short-latency communication scenarios.
15 Oct 2020
TL;DR: 5G NR LDPC is 1 dB closer to the Shannon limit than WLAN LDPCs, but this gain is lost for short message lengths as the ones used in Factory Automation environments, and latency results are promising due to the opportunity of combining the analyzed techniques with new MAC techniques in order to achieve the desired reliability while not affecting latency dramatically.
Abstract: Critical application requirements proposed for Factory Automation scenarios involve demanding and simultaneous restrictions in reliability and latency. Channel coding is a basic tool to guarantee reliability but it usually involves high computation and memory resources at both transmitting and receiving sides. Among all the possible choices, Low Density Parity Check codes provide outstanding correction capacity. This paper studies two different LDPC coding approaches: 5G New Radio (5G NR) and IEEE 802.11 (WLAN). One of the drawbacks of LDPCs is their degraded performance and complex matrix adaptation for short information packets. Both 5G and 802.11 LDPCs use Quasi-Cyclic LDPC as the adaptation technique for matching the data packet size and coding matrix dimension. This paper evaluates 5G and 802.11 LDPC techniques, analyzing their structure and reliability performance for very short information messages by means of simulations. The results show that 5G NR LDPC is 1 dB closer to the Shannon limit than WLAN LDPCs, but this gain is lost for short message lengths as the ones used in Factory Automation environments. However, latency results are promising due to the opportunity of combining the analyzed techniques with new MAC techniques in order to achieve the desired reliability while not affecting latency dramatically.
27 Oct 2020
TL;DR: In this paper, the authors proposed a certain circular structured constraint strategy to design one dimensional non-uniform constellations (1D-NUCs) with remarkable performance, which benefits applications in power-limited systems.
Abstract: Adopting higher modulation order and spacing constellation symbols non-uniformly are two strategies in modern communication systems to meet increasing demand for data volume and to reduce the gap between bit-interleaved coded modulation (BICM) capacity and Shannon limit. This paper proposes a certain circular structured constraint strategy to design one dimensional non-uniform constellations (1D-NUCs) with remarkable performance. This strategy also ensures low demapping complexity (especially for high order NUCs) which benefits applications in power-limited systems. Meanwhile, a computable expression of BICM capacity based on polar coordinates is derived to revise constellation designing scheme with the proposed constraint strategy. Through the revised designing scheme, a set of circular structured 1D-NUCs with order of 1024 are obtained and testified having the ability to provide higher shaping gain than the ones adopted by ATSC 3.0 with low complexity.
01 Jan 2020
TL;DR: In this paper, information theoretic tools are used to design communication systems with coded modulation and probabilistic shaping (PS) that operate close to the Shannon limit, and applications of PS are investigated for optical communications.
Abstract: Information theoretic tools are used to design communication systems with coded modulation and probabilistic shaping (PS) that operate close to the Shannon limit. Probabilistic amplitude shaping is introduced for channels with a symmetric capacity-achieving distribution and geometric shaping is discussed. Binary and non-binary low-density parity-check codes are designed considering various constraints and target rates. Finally, applications of PS are investigated for optical communications.
TL;DR: The way of multi-rate LDPC decoding is explored through theoretical analysis and simulation results, and the decoding aspects and performance of LDPC codes are analyzed and compared according to the bit error rate.
Abstract: Low-density parity-check code (LDPC) not only has good performance approaching the Shannon limit, but also has low decoding complexity and flexible structure. It is a research hot-spot in the field of channel coding in recent years and has a wide range of application prospects in optical communication systems. In this paper, the decoding aspects and performance of LDPC codes are analyzed and compared according to the bit error rate (BER) of LDPC codes. The computer simulation was carried out under additive white Gaussian noise (AWGN) channel and binary phase shift keying (BPSK) modulation. Through theoretical analysis and simulation results, this paper explores the way of multi-rate LDPC decoding.
Patent•
23 Oct 2020
TL;DR: In this paper, the authors proposed a discrete modulation signal MIMO transmission method, which is mainly characterized by the mutual information of symbol vectors of a sending end and a receiving end is maximized through the joint optimization of signal source distribution and a precoding matrix, so that the transmission rate is close to the Shannon limit.
Abstract: The invention provides a discrete modulation signal MIMO transmission method, which is mainly characterized in that the mutual information of symbol vectors of a sending end and a receiving end is maximized through the joint optimization of signal source distribution and a precoding matrix, so that the transmission rate is close to the Shannon limit. The method comprises the steps of: under the condition that the current precoding matrix G is determined, optimizing the distribution of the information source vector x, and maximizing the information source entropy through adoption of a Lagrangenumber multiplication method; and under the condition that the current information source vector distribution is determined, optimizing the precoding matrix G through adoption of a gradient descent method to maximize the mutual information of the sending vector and the receiving vector. The transmission rate close to the Shannon limit is realized in an MIMO scene through joint optimization of information source distribution and a precoding matrix. The sending end determines the edge distribution of each path of symbol and then performs non-uniform modulation by adopting a probability amplitudeforming technology. On the basis of the existing single-path probability amplitude forming technology, the characteristics of the MIMO system are combined, and the maximum error-free transmission rate for the MIMO scene is theoretically realized.
01 Apr 2020
TL;DR: The main goal of this paper is to review as simple as possible the statistical properties of LDPC codes, and how it is used especially facing the decoding problem.
Abstract: In this paper, the LDPC (Low Density Parity Check Codes) decoding algorithm has been investigated using statistical mechanics properties. The main advantage of LDPC codes is their performance that works in near Shannon limit, and the ability to use iterative decoding algorithms. In 1989 N. Sourlas showed that error-correcting codes can be considered as Spin-Glass systems thus making it possible to model LDPC codes as an Ising model, opening the way for information theorists to solve coding problems with the power of statistical mechanics. According to N. Sourlas, the decoding problem can be solved by finding the ground state of the corresponding spin-system Hamiltonian. The main goal of this paper is to review as simple as possible the statistical properties of LDPC codes, and how it is used especially facing the decoding problem.
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TL;DR: This paper presents a construction of LDPC codes from cubic symmetric graphs, and analyses properties of the obtained codes and presents bounds for the code parameters, the dimension and the minimum distance.
Abstract: Low-density parity-check (LDPC) codes have been the subject of much interest due to the fact that they can perform near the Shannon limit. In this paper we present a construction of LDPC codes from cubic symmetric graphs. The constructed codes are $(3,3)$-regular and the vast majority of the corresponding Tanner graphs have girth greater than four. We analyse properties of the obtained codes and present bounds for the code parameters, the dimension and the minimum distance. Furthermore, we give an expression for the variance of the syndrome weight of the constructed codes. Information on the LDPC codes constructed from bipartite cubic symmetric graphs with less than 200 vertices is presented as well. Some of the constructed codes are optimal, and some have an additional property of being self-orthogonal or linear codes with complementary dual (LCD codes).
23 May 2020
TL;DR: A synchronization scheme for BDS B2a signal by utilizing the information from the process of decoding using the decoding result of the Extended Min-Sum (EMS) algorithm.
Abstract: Low-Density Parity-Check (LDPC) Code has become one of the best coding technologies at present because of its low complexity iterative decoding algorithm and its performance with further close to the Shannon limit. Non-binary LDPC codes designed in high order Galois fields have shown better potential than binary LDPC codes with the same code length and code rate, therefore it was applied for the navigation message encoding in BeiDou satellite navigation system (BDS). The navigation message contains time information, ephemeris parameters, clock correction terms and so forth, which is necessary for navigation solution. As the synchronization head was not encoded, it is hard to deal with data synchronization and navigation data decoding when the navigation receiver works at a low Signal-to-Noise Ratio (SNR). Aiming at this problem, we present a synchronization scheme for BDS B2a signal by utilizing the information from the process of decoding. The synchronizer is based on syndrome checks using the decoding result of the Extended Min-Sum (EMS) algorithm. Ratios of satisfaction of all check restrictions are computed firstly, and then the boundary value is obtained through MonteCarlo method. Simulation results show that the proposed algorithm performs well at relatively low SNR compared with traditional method.
05 Sep 2020
TL;DR: In this article, the authors compared all the forward error-correcting codes and found the optimum channel code for the 5G mobile communication system, which may lead to the key channel codes, for data and control in the fifth-generation new radio communication (5G NR communication) should stand with high flexibility, low complexity, high reliability, high throughput, and very important much low latency for mMTC and URLLC.
Abstract: In the era of digital communication, various codes have been used for channel codings like convolution, trellis, turbo, LDPC, and polar codes for error detection and correction. Convolution and turbo codes are the earlier codes used for high energy efficiency for short length communication like machine-type communication (MTC), control purpose of the broadband (MBB) and also for reliability and latency purpose (URLLC). But these codes have the limitation of working for short block length message transmission. To solve these problems, LDPC codes are used which are constructed from the protograph matrix. It is helpful to generate and create a strong matrix form of long block length data transmission with a sparse matrix. LDPC code has a good error performance near to Shannon limit at high SNR with low complexity than other codes but does not perfectly satisfy the URLLC requirement in 5G NR communications. A new candidate polar code is introduced and is a sequential control channel used for low latency for short length message transmission. The purpose of the paper is to survey the comparison between flexibility, complexity, reliability, throughput, latency, and efficiency between various channel codes. Specifically, the comparison of LDPC and polar codes, which may lead to the key channel codes, for data and control in the fifth-generation new radio communication (5G NR communication) should stand with high flexibility, low complexity, high reliability, high throughput, and very important much low latency for mMTC and URLLC. Hence, in this paper, we are comparing all the forward error-correcting codes and finding optimum channel code for the 5G mobile communication system.
13 Nov 2020
TL;DR: In this paper, parallelly concatenated spatially coupled RA (PC-SCRA) codes were presented based on SCRA codes with the advantages of simple coding structure, threshold saturation and low decoding complexity.
Abstract: In this paper, parallelly concatenated spatially coupled RA (PC-SCRA) codes was presented based on spatially coupled RA (SCRA) codes with the advantages of simple coding structure, threshold saturation and low decoding complexity When encoding, the same message bits are respectively encoded by two same SCRA codes to obtain respective check bits During transmission, the message bits and the obtained parity bits are merged into one codeword for transmission Besides, density evolution algorithm was proposed to compute the iterative decoding threshold of PC-SCRA code ensemble over the binary erasure channel Simulation results show that the proposed PC-SCRA code ensemble has excellent BP threshold performance close to Shannon limit and is superior to the spatially coupled LDPC (SC-LDPC) code with same coderate, which provides a new way for construrting capacity-approaching SC-LDPC codes
TL;DR: In this article, a construction of LDPC codes from cubic symmetric graphs is presented, where the codes constructed are (3, 3)-regular and the vast majority of the corresponding Tanner graphs have girth greater than four.
Abstract: Low-density parity-check (LDPC) codes have been the subject of much interest due to the fact that they can perform near the Shannon limit. In this paper we present a construction of LDPC codes from cubic symmetric graphs. The codes constructed are (3, 3)-regular and the vast majority of the corresponding Tanner graphs have girth greater than four. We analyse properties of the codes obtained and present bounds for the code parameters, the dimension and the minimum distance. Furthermore, we give an expression for the variance of the syndrome weight of the codes constructed. Information on the LDPC codes constructed from bipartite cubic symmetric graphs with less than 200 vertices is presented as well. Some of the codes constructed are optimal, and some have an additional property of being self-orthogonal or linear codes with complementary dual (LCD codes).
27 Oct 2020
TL;DR: In this article, the performance of bit-interleaved Coded Modulation (BICM) in DOCSIS 3.1 and 4.0 was analyzed and it was shown that there is a gap of approximately 3.5 dB between the theoretical Shannon limit and the actual Shannon limit.
Abstract: The Data Over Cable Service Interface Specification (DOCSIS) provides Internet access via Hybrid Fiber Coax networks. The current version DOCSIS 3.1 and the planned next iteration DOCSIS 4.0 use Quadrature Amplitude Modulation (QAM) and Low-Density Parity Check (LDPC) codes for Bit-Interleaved Coded Modulation (BICM). This paper analyzes the BICM performance characteristics of the DOCSIS downstream. We find that there is a gap of approximately 3.5 dB between DOCSIS and the theoretical Shannon limit. To reduce this gap, we suggest the use of alternative LDPC codes and Non-Uniform Constellations (NUCs) as specified by the ATSC 3.0 standard. To adjust the ATSC 3.0 specification for cable networks, we introduce novel NUCs that target very high signal-to-noise ratios. The proposed BICM chain reduces the distance to the Shannon limit by up to 1 dB.
19 Oct 2020
TL;DR: In this paper, an algorithm is proposed to find the positions of the symbols in QAM modulations that maximize capacity, generating the non-uniform QAM (NQAM) modulations.
Abstract: Currently with the growth in traffic in wireless networks and with services that require higher speed, the challenge of reaching Shannon’s limit remains a topic of great interest, so that, seeking to increase the capacity BICM of a channel allows the use of better performing channel codes approaching the Shannon limit. The article presents an algorithm proposal to find the positions of the symbols in QAM modulations that maximize capacity, generating the Non Uniform QAM modulations. Additionally, symbol positions are presented to maximize capacity and keep average symbol energy constant. It is validated that this increase in capacity doesn’t affect the bit error rate in an AWGN channel.