Rate-compatible Low-density Parity-check Codes Research Articles

Experimental demonstration of flexible information rate PON beyond 100 Gb/s with rate-compatible LDPC codes

The applications of rate-compatible low-density parity-check (RC-LDPC) codes are investigated for a 16 quadrature amplitude modulation (16QAM) signal and coherent detection system. With rate-compatible signals, we can provide the flexible net data rate between 135.5 Gb/s and 169.7 Gb/s in a passive optical network (PON) link. Based on the LDPC codes defined in the IEEE 802.3ca standard, we construct two sets of RC-LDPC codes with a fixed and variable information bit length. Since the puncturing operation may degrade the performance of LDPC codes, we apply the protograph-based extrinsic information transfer (PEXIT) technique to optimize the puncturing positions to mitigate the degradation. Additionally, we explore four low-complexity LDPC decoding algorithms (min sum, offset min sum, variable weight min sum, and relaxed min sum with 2 nd min emulation) to investigate the relationship between the computational complexity and decoding performance. Simulation results indicate that the constructed codewords exhibit good performance in the waterfall region across a range of code rates. Finally, we conduct an experimental setup in a dual-polarization 25 GBaud 16QAM coherent PON to verify the effectiveness of the constructed LDPC codes with four decoding algorithms. The experimental results show maximal 4.8 dB receiver sensitivity differences, which demonstrate the feasibility of the method for constructing RC-LDPC codes in future high-speed flexible coherent PON.

Memory Efficient Mutual Information-Maximizing Quantized Min-Sum Decoding for Rate-Compatible LDPC Codes

In this letter, we propose a two-stage design method to construct memory efficient mutual information-maximizing quantized min-sum (MIM-QMS) decoder for rate-compatible low-density parity-check (LDPC) codes. We first develop a modified density evolution to design a unique set of lookup tables (LUTs) that can be used for rate-compatible LDPC codes. The constructed LUTs are optimized based on their discrepancy values and a merge function to reduce the memory requirement. Numerical results show that the proposed rate-compatible MIM-QMS decoder can reduce the memory requirement for decoding by up to 94.92 % compared to the benchmark rate-compatible LUT-based decoder with generally faster convergence speed. In addition, the proposed decoder can approach the performance of the floating-pointing belief propagation decoder within 0.15 dB.

Rate-compatible multi-edge type low-density parity-check code ensembles for continuous-variable quantum key distribution systems

In this paper, we propose a design rule of rate-compatible punctured multi-edge type low-density parity-check (MET-LDPC) code ensembles with degree-one variable nodes for the information reconciliation (IR) of continuous-variable quantum key distribution (CV-QKD) systems. In addition to the rate compatibility, the design rule effectively resolves the high error-floor issue which has been known as a technical challenge of MET-LDPC codes at low rates. Thus, the proposed design rule allows one to implement rate-compatible MET-LDPC codes with good performances both in the threshold and low-error-rate regions. The rate compatibility and the improved error-rate performances significantly enhance the efficiency of IR for CV-QKD systems. The performance improvements are confirmed by comparing complexities and secret key rates of IR schemes with MET-LDPC codes whose ensembles are optimized with the proposed and existing design rules. In particular, the SNR range of positive secrecy rate increases by 1.44 times, and the maximum secret key rate improves by 2.10 times as compared to the existing design rules. The comparisons clearly show that an IR scheme can achieve drastic performance improvements in terms of both the complexity and secret key rate by employing rate-compatible MET-LDPC codes constructed with code ensembles optimized with the proposed design rule.

Reliability‐based quantization for soft decoding of LDPC codes in short‐reach optical links

Efficient quantizer design is vital in high-speed optical receivers. In this paper, the authors propose a three-level (1.5-bit) reliability-based quantizer for low-complexity soft decoding of low-density parity-check (LDPC) codes, and show that it outperforms a conventional quantizer employing eight levels (3 bits). Different approaches for obtaining the quantization thresholds are discussed, and it is shown that the achievable channel capacity with the proposed quantizer is within 0.4 dB of the Shannon limit of the unquantized channel. Rate-compatible LDPC codes are also designed tailored to the asymmetric optical channel terminated with the proposed reliability-based quantizer, and it is shown that the resulting quantizer-aware LDPC codes significantly outperform other existing codes of similar rates.

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.

Performance Analysis and Code Optimization of IDMA With 5G New Radio LDPC Code

In this letter, we focus on the performance analysis and code optimization of interleave-division multiple access (IDMA) with the rate-compatible low-density parity-check (LDPC) code adopted in 5G new radio (5G-NR) technical specification. By combining the multi-edge type density evolution (DE) and extrinsic information transfer (EXIT) analysis, a multi-edge-type DE-aided EXIT analysis is developed to analyze the asymptotic performance of 5G-NR LDPC-coded IDMA, which is shown to be fairly robust against the variations of user number. Then, the base matrix of 5G-NR LDPC code is optimized for IDMA to achieve higher sum spectral efficiency while maintaining the rate compatibility.

Rate‐compatible ARACA codes

A design method for rate-compatible (RC) accumulate repeat accumulate check accumulate (ARACA) codes as protograph-based RC low-density parity-check codes is presented. The proposed RC-ARACA codes provide not only good iterative decoding thresholds with the linear minimum distance growth property but also efficient encoder/decoder structures with low complexities, so that they are appropriate to ultra-reliable and low latency communication services for fifth generation.

Low latency IR-HARQ for multiband WLAN system

This paper proposes a low latency incremental redundancy hybrid ARQ (IR-HARQ) scheme for a multiband wireless local area network (WLAN) system. The proposed scheme can reduce a retransmission delay and ensure backward compatibility with WLAN devices by using a clear to send (CTS) frame of a current WLAN system and rate compatible low-density parity-check (RC-LDPC) codes. Additionally, it can minimize the retransmission delay by selecting an optimal retransmission data length on the basis of the accumulated mutual information (ACMI) for available frequency bands. The results of computer simulations show that the multiband WLAN system using the proposed scheme has shorter retransmission delay and higher system throughput than the current WLAN system.

A non-greedy puncturing method for rate-compatible LDPC codes

In this paper, we propose a non-greedy punctur- ing method for constructing binary rate-compatible low-density parity-check codes. First, we show that the recovery error prob- ability for a punctured variable node can be reduced by allocat- ing a small number of unpunctured variable nodes in the recovery tree. Then, we redefine the recovery tree according to the princi- ple of iterative decoding with the sum-product algorithm. The pro- posed non-greedy puncturing algorithm lies mainly in the dynam- ical minimization of the number of unpunctured variable nodes in the redefined recovery tree for the punctured variable nodes. Fi- nally, simulation results show that the proposed puncturing algo- rithm outperforms the existing best puncturing algorithms in bit error rate performances of iterative decoding.

FPGA-Based Rate-Compatible LDPC Codes for the Next Generation of Optical Transmission Systems

In this paper, we propose a rate-compatible forward error-correcting (FEC) scheme based on low-density-parity check (LDPC) codes together with its software reconfigurable unified field-programmable gate array (FPGA) architecture. By FPGA emulation, we demonstrate that the proposed class of rate-compatible LDPC codes based on puncturing and generalized LDPC coding with an overhead from 25% to 46% provides a coding gain ranging from 12.67 to 13.8 dB at a post-FEC bit-error rate (BER) of 10−15. As a result, the proposed rate-compatible codes represent one of the strong FEC candidates of soft-decision FEC for both short-haul and long-haul optical transmission systems.

An Encoder with Speed over 40Gbps for RC LDPC Codes with Rates Up to 0.96

We propose a class of Rate-compatible (RC) Low-density parity-check (LDPC) codes with a very wide range of code rates. To widen the range of rates, we have developed an optimal transmission scheme to push the upper bound of code rates to 0.96. Characterized by a parity check matrix in a dual-diagonal form, the proposed RC LDPC code can be encoded in linear time. Constructed from shifted identity sub-matrices, the proposed codes are particularly well-suited for the high-speed implementation of parallel encoders. Furthermore, the encoder can be implemented efficiently with several left circular shifters and XOR gates. To maximize the encoding speed, we have proposed a q-parallel encoder architecture, where q is the size of each sub-matrix. The implementation results into Field programmable gate array (FPGA) devices indicate that a 72-parallel encoder for the proposed RC LDPC code with a code rate from 0.5 to 0.96 is capable of reaching a speed of 42 Gigabits per second (Gbps) using a clock frequency of 300MHz.

A Combined Algebraic- and Graph-Based Method for Constructing Structured RC-LDPC Codes

This letter presents a new method for constructing rate-compatible low-density parity-check (RC-LDPC) codes, which is based on combining algebraic-based and graph-based construction methods. We first use a graph-based tool, protograph extrinsic information transfer chart, to construct a masking matrix. Then, the parity-check matrices of RC-LDPC codes are determined in accordance with the framework of the algebraic-based method. The proposed codes own a quasi-cyclic structure, and thus have advantages in hardware implementations of encoder and decoder. Simulation results show that the codes can achieve good bit error rate performance in the waterfall region within a wide range of code rates.

Rate-compatible LDPC codes based on the PEG algorithm for relay communication systems

It is known that the progressive edge-growth (PEG) algorithm can be used to construct low-density parity-check (LDPC) codes at finite code lengths with large girths through the establishment of edges between variable and check nodes in an edge-by-edge manner. In [1], the authors derived a class of LDPC codes for relay communication systems by extending the full-diversity root-LDPC code. However, the submatrices of the parity-check matrix H corresponding to this code were constructed separately; thus, the girth of H was not optimized. To solve this problem, this paper proposes a modified PEG algorithm for use in the design of large girth and full-diversity LDPC codes. Simulation results indicated that the LDPC codes constructed using the modified PEG algorithm exhibited a more favorable frame error rate performance than did codes proposed in [1] over block-fading channels.

Protograph-Based Raptor-Like LDPC Codes

This paper proposes protograph-based Raptor-like (PBRL) codes as a class of rate-compatible low-density parity-check codes for binary-input AWGN channels. As with the Raptor codes, exclusive-OR operations on precoded bits produce additional parity bits providing extensive rate compatibility. Unlike Raptor codes, each additional parity bit in the protograph is explicitly designed to optimize the density evolution threshold. During the lifting process, approximate cycle extrinsic message degree (ACE) and circulant progressive edge growth (CPEG) constraints are used to avoid undesirable graphical structures. Some density-evolution performance is sacrificed to obtain lower error floors, particularly at short block-lengths. Simulation results are shown for information block sizes of k = 1032 and 16 384. For a target frame error rate of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> , at each rate, the k = 1032 and 16 384 code families perform within 1 dB and 0.4 dB of both the Gallager bound and the normal approximation, respectively. The 16 384 code family outperforms the best known standardized code family, namely, the AR4JA codes. The PBRL codes also outperform DVB-S2 codes that have the advantages of longer blocklengths and outer BCH codes. Performance is similar to RC code families designed by Nguyen et al. that do not constrain codes to have the PBRL structure and involve simulation in the optimization process at each rate.

Jointly optimized rate-compatible UEP-LDPC codes for half-duplex co-operative relay networks

This paper addresses the design of low-density parity-check (LDPC) codes for half-duplex co-operative relay networks. Structured rate-compatible codes with unequal error protection (UEP) are designed through joint optimization of the codes for the channels between source and relay and source and destination. The proposed codes clearly outperform simpler LDPC codes which are not optimized for relay channels and puncturing-based rate-compatible LDPC codes, and they show a significant performance improvement over the direct link communication depending on the position of relay. The optimization algorithm for the proposed codes is based on density evolution using the Gaussian approximation and optimal variable node degree distributions are found through iterative linear programming. Interestingly, they anyhow show performance which is almost comparable to the performance of codes optimized through a more complex non-linear optimization algorithm. We analyze the performance of our proposed codes with short, medium and long block lengths, and with low and high rates under realistic assumptions, i.e., imperfect decoding of the codeword at relay and variant signal-to-noise ratio within a single codeword.

EXIT-Based Side Information Refinement in Wyner–Ziv Video Coding

The accuracy of the side information (SI) is critical in the performance of distributed video coding algorithms. The SI is typically built at a decoder based on the reconstructed data and on channel coding parity bits transmitted by the encoder. The optimal encoding rate is generally difficult to compute precisely due to the dynamics of video content with varying correlation. Effective methods for the refinement of imprecise SI are therefore important for improved decoding quality. In this paper, we propose to exploit the intrinsic property of channel coding algorithms in Wyner-Ziv video coding. The SI is refined via both the information-plane and the parity-plane bits, which rapidly increases the accuracy of refined SI. We use extrinsic information transfer chart analysis in order to estimate the variations of the mutual information in the iterative decoding. In particular, we characterize mutual information variations for punctured regular and irregular rate-compatible low-density parity-check codes. Tracking the mutual information changes permits to decrease the coding rate of the information and parity bitstreams, while preserving the decoding quality. Simulation results confirm that our method improves on the decoding quality of recent distributed video coding algorithms, especially for high-motion sequences or at high-coding rate regimes.

LDPC codes for soft decode-and-forward in half-duplex relay channels

We investigate the use of rate-compatible lowdensity parity-check (RC-LDPC) codes as part of a soft decodeand- forward (SDF) protocol over the half-duplex relay channel. We propose a new methodology to design the degree distribution of the RC-LDPC codes with a lower triangular parity-check matrix, enabling the additional parity bits to be linearly and systematically encoded at the relay. Our proposed methodology introduces the concept of a K-layer doping matrix to represent the structure of a lower triangular parity-check matrix. As a result of our methodology, the asymptotic performance of RC-LDPC codes can be analyzed and predicted using the multi-edge-type density evolution. Then, we derive the soft-re-encoding of the additional parity symbols at the relay using our designed RCLDPC codes. Moreover, we propose a novel method, which we refer to as soft fading, to compute the log-likelihood ratio (LLR) of the received signal at the destination for the SDF protocol. We demonstrate that our proposed soft fading method outperforms the best known method in the literature by up to 0.7 dB in terms of BER performance. Finally, we derive a new bound for the power multiplication factor at the relay, which limits the amount of soft-errors forwarded by the relay to the destination. The BER performance of our new RC-LDPC codes improves significantly once the power multiplication factor at the relay satisfies this bound.

Managing Imperfect Spectrum Sensing in the Secondary Service: Increasing Sensing Time or Adopting Channel Coding?

Imperfect spectrum sensing in overlay spectrum sharing may cause collision between primary and secondary transmission resulting in performance degradation for primary users. To satisfy the quality of service requirement imposed by the primary service, the maximum probability of collision has to be kept below a given threshold. The collision, if occurs, also results in increasing error rate in the secondary system. What can be done if the secondary service needs better error rate than the value imposed by the collision constraint in the primary network? From secondary user perspective, this can be taken care of by employing channel coding techniques at the expense of effective rate reduction. Alternatively, one can increase the sensing time to reduce the collision probability at the expense of reducing the data transmission time. This also reduces the effective data rate for secondary users. In this letter, we compare these two approaches and demonstrate a situation where using rate-compatible Low-Density Parity-Check codes, the effective data rate for the coded case can be significantly more than that of the case without channel coding while exhibiting a considerably better performance. We then discuss necessary condition for such an advantage and come up with cases where increasing sensing time is preferred over adopting channel coding.

Channel Modelling Scheme for UWB with Multiple Antennas Using Ray-Tracing Approach for Rate-Compatible Low-Density Parity-Check Codes

The work in this paper can be broadly divided into three distinct parts. In first part of this work, a deterministic channel model is developed using the art of computer game technology. The developed system can compute the impulse response of an indoor environment. First, both reflection and refraction phenomenon were considered followed by the frequency effect on the channel impulse response (CIR) analysis for 500 MHz to 4 GHz range. In the second part of the work, the designed channel model is extended to inherent antenna diversity. An efficient MIMO-UWB channel modelling scheme is implemented based on the above-mentioned channel model. First, the channel is simulated using single antenna on both sides of the system. The dense multipath channel of UWB is then efficiently exploited using different configuration of multiple antennas on both sides. Simulation results show great improvement in CIR for multiple antennas case. The last part of the work is aimed at testing the model for low-density parity-check (LDPC) codes. The results show the consistency and fine compatibility of our model under LDPC coding system.

LDPC codes for soft decode-and-forward in half-duplex relay channels

We investigate the use of rate-compatible lowdensity parity-check (RC-LDPC) codes as part of a soft decodeand- forward (SDF) protocol over the half-duplex relay channel. We propose a new methodology to design the degree distribution of the RC-LDPC codes with a lower triangular parity-check matrix, enabling the additional parity bits to be linearly and systematically encoded at the relay. Our proposed methodology introduces the concept of a K-layer doping matrix to represent the structure of a lower triangular parity-check matrix. As a result of our methodology, the asymptotic performance of RC-LDPC codes can be analyzed and predicted using the multi-edge-type density evolution. Then, we derive the soft-re-encoding of the additional parity symbols at the relay using our designed RCLDPC codes. Moreover, we propose a novel method, which we refer to as soft fading, to compute the log-likelihood ratio (LLR) of the received signal at the destination for the SDF protocol. We demonstrate that our proposed soft fading method outperforms the best known method in the literature by up to 0.7 dB in terms of BER performance. Finally, we derive a new bound for the power multiplication factor at the relay, which limits the amount of soft-errors forwarded by the relay to the destination. The BER performance of our new RC-LDPC codes improves significantly once the power multiplication factor at the relay satisfies this bound.