Construction of Regular Rate-Compatible LDPC Convolutional Codes

In this paper, we propose a new method to derive a family of regular rate-compatible low-density parity-check（RC-LDPC） convolutional codes from RC-LDPC block codes. In the RC-LDPC convolutional family, each extended sub-matrix of each extended code is obtained by choosing specified elements from two fixed matrices HE1K and HE1K, which are derived by modifying the extended matrices HE1 and HE2 of a systematic RC-LDPC block code. The proposed method which is based on graph extension simplifies the design, and prevent the defects caused by the puncturing method. It can be used to generate both regular and irregular RC-LDPC convolutional codes. All resulted codes in the family are systematic which simplify the encoder structure and have maximum encoding memories which ensure the property. Simulation results show the family collectively offer a steady improvement in performance with code compatibility over binary-input additive white Gaussian noise channel（BI-AWGNC）.

Design of Irregular QC-LDPC Code Based Multi-Level Coded Modulation Scheme for High Speed Optical Communication Systems

In this paper, we focus on the design of irregular QC-LDPC code based multi-level coded modulation(MLCM) scheme by jointly optimizing the component code rate and the degree distribution of the irregular QC-LDPC component code. Firstly, the sub-channel capacities of MLCM systems is analyzed and discussed, based on which the optimal component code rate can be obtained. Secondly, an extrinsic information transfer chart based two-stage searching algorithm is proposed to find the good irregular QC-LDPC code ensembles with optimal component code rates for their corresponding sub-channels. Finally, by constructing the irregular QC-LDPC component codes from the designed ensembles with the aim of possibly enlarging the girth and reducing the number of the shortest cycles, the designed irregular QC-LDPC code based 16QAM and 64QAM MLCM systems can achieve 0.4 dB and 1.2 dB net coding gain, respectively, compared with the recently proposed regular QC-LDPC code based 16QAM and 64QAM MLCM systems.

Design of good QC-LDPC codes without small girth in the p-plane

A construction method based on the p-plane to design high-girth quasi-cyclic low-density parity-check （QC-LDPC） codes is proposed. Firstly the good points in every line of the p-plane can be ascertained through filtering the bad points, because the designed parity-check matrixes using these points have the short cycles in Tanner graph of codes. Then one of the best points from the residual good points of every line in the p-plane will be found, respectively. The optimal point is also singled out according to the bit error rate （BER） performance of the QC-LDPC codes at last. Explicit necessary and sufficient conditions for the QC-LDPC codes to have no short cycles are presented which are in favor of removing the bad points in the p-plane. Since preventing the short cycles also prevents the small stopping sets, the proposed construction method also leads to QC-LDPC codes with a higher stopping distance.

Some Explicit Constructions of Type-Ⅱ,Ⅲ,Ⅳ,Ⅴ QC-LDPC Codes with Girth 6

Multi-type quasi-cyclic(QC) low-density parity-check(LDPC) codes can be considered as multiple-edge protograph QC-LDPC codes having some advantages in the minimum Hamming distance bound over single-edge protograph codes or type-Ⅰ QC-LDPC codes when the base matrices have the same size. In this paper, we investigate a class of multi-type QC-LDPC codes whose parity-check matrices contain just one blockrow of circulants and we obtain the generator matrix of such codes in general form. Using the permutation arrays and defining injection arrays, we present a new approach to construct a class of high-rate type-Ⅰ QC-LDPC codes with girth 6 from the constructed 4-cycle free multi-type QC-LDPC codes. In continue, for 2 ≤ w≤6, some type-w QC-LDPC codes with girth 6 are constructed explicitly such that the constructed codes are flexible in terms of rate and length. To the best of our knowledge, for w = 5,6, this is the first paper which deals with the explicit construction of type-w QC-LDPC codes with girth 6 and high rates. Moreover, for w = 3, 4, the constructed type-w QC-LDPC codes have better(6,8)-cycle multiplicities than the codes with minimum achievable length recently constructed by cyclic difference families(CDFs). Simulation results show that the binary and non-binary constructed codes outperform the constituent underlying QC-LDPC codes.

Two-Stage Constructions for the Rate-Compatible Shortened Polar Codes

In this paper,we propose the two-stage constructions for the rate-compatible shortened polar(RCSP)codes.For the Stage-I construction,the shortening pattern and the frozen bit are jointly designed to make the shortened bits be completely known by the decoder.Besides,a distance-greedy algorithm is presented to improve the minimum Hamming distance of the codes.To design the remaining Stage-II frozen bits,three different construction algorithms are further presented,called the Reed-Muller(RM)construction,the Gaussian Approximation(GA)construction,and the RM-GA construction.Then we give the row weight distribution numerical results of the generator matrix after the Stage-I and Stage-II constructions,which shows that the proposed constructions can efficiently increase the minimum Hamming distance.Simulation results show that the proposed RCSP codes have excellent frame error rate(FER)performances at different code lengths and code rates.More specifically,the RM-GA construction performs best and can achieve at most 0.8 dB gain compared to the Wang14 and the quasi-uniform puncturing(QUP)schemes.The RM construction is designed completely by the distance-constraint without channel evaluation thus has the simplest structure.Interestingly,it still has better FER performance than the existing shortening/puncturing schemes,especially at high signal noise ratio(SNR)region.

Construction of Quasi-Cyclic Low-Density Parity-Check Codes for Simplifying Shuffle Networks in Layered Decoder

Offset Shuffle Networks(OSNs) interleave a-posterior probability messages in the Block Row-Layered Decoder(BRLD) of QuasiCyclic Low-Density Parity-Check(QC-LDPC)codes.However,OSNs usually consume a significant amount of computational resources and limit the clock frequency,particularly when the size of the Circulant Permutation Matrix(CPM)is large.To simplify the architecture of the OSN,we propose a Simplified Offset Shuffle Network Block Progressive Edge-Growth(SOSNBPEG) algorithm to construct a class of QCLDPC codes.The SOSN-BPEG algorithm constrains the shift values of CPMs and the difference of the shift values in the same column by progressively appending check nodes.Simulation results indicate that the error performance of the SOSN-BPEG codes is the same as that of the codes in WiMAX and DVB-S2.The SOSNBPEG codes can reduce the complexity of the OSNs by up to 54.3%,and can improve the maximum frequency by up to 21.7%for various code lengths and rates.

On Cross-Layer Design of AMC Based on Rate Compatible Punctured Turbo Codes

This paper extends the work on cross-layer design which combines adaptive modulation and coding at the physical layer and hybrid automatic repeat request protocol at the data link layer. By contrast with previous works on this topic, the present development and the performance analysis as well, is based on rate compatible punctured turbo codes. Rate compatibility provides incremental redundancy in transmission of parity bits for error correction at the data link layer. Turbo coding and iterative decoding gives lower packet error rate values in low signal-to-noise ratio regions of the adaptive modulation and coding (AMC) schemes. Thus, the applied cross-layer design results in AMC schemes can achieve better spectral efficiency than convolutional one while it retains the QoS requirements at the application layer. Numerical results in terms of spectral efficiency for both turbo and convolutional rate compatible punctured codes are presented. For a more comprehensive presentation, the performance of rate compatible LDPC is contrasted with turbo case as well as the performance complexity is discussed for each of the above codes.

Design of Raptor Design of Raptor-Like Rate Compatible SC Like Rate Compatible SC-LDPC Codes

This paper proposes a family of raptor-like rate-compatible spatially coupled low-density parity-check(RL-RC-SC-LDPC)codes from RL-RC-LDPC block codes.There are two important keys.One is the performance of the base matrix.RL-LDPC codes have been adopted in the technical specification of 5G new radio(5G-NR).We use the 5G NR LDPC code as the base matrix.The other is the edge coupling design.In this regard,we have designed a rate-compatible coupling algorithm,which can improve performance under multiple code rates.The constructed RL-RC-SC-LDPC code property requires a large coupling length L and thus we improved the reciprocal channel approximation(RCA)algorithm and proposed a sliding window RCA algorithm.It can provide lower com-plexity and latency than RCA algorithm.The code family shows improved thresholds close to the Shannon limit and finite-length performance compared with 5G NR LDPC codes for the additive white Gaussian noise(AWGN)channel.

Construction of Rate-Compatible(RC) Low-Density Parity-Check(LDPC) Convolutional Codes Based on RC-LDPC Block Codes

In this paper,a family of rate-compatible(RC) low-density parity-check(LDPC) convolutional codes can be obtained from RC-LDPC block codes by graph extension method.The resulted RC-LDPC convolutional codes,which are derived by permuting the matrices of the corresponding RC-LDPC block codes,are systematic and have maximum encoding memory.Simulation results show that the proposed RC-LDPC convolutional codes with belief propagation(BP) decoding collectively offer a steady improvement on performance compared with the block counterparts over the binary-input additive white Gaussian noise channels(BI-AWGNCs).

Fiber-based optical parametric amplifier for 40-Gb/s NRZ-DPSK signal transmission system employing QC-LDPC codes

In this letter, we investigate quasi-cyclic low-density parity-check （QC-LDPC） codes in a 40-Gb/s nonreturn-to-zero differential phase-shift keying （NRZ-DPSK） signal transmission system based on a fiber- based optical parametric amplifier （FOPA）. A constructed algorithm of QC-LDPC codes according to the optimizing set of shift vMues on the circulant permutation matrix （CPM） of the basis matrix is proposed. Simulation results prove that the coding gain in the encoded system can be realized at 10.2 dB under QC- LDPC codes with a code rate of 5/6 when the bit error rate （BER） is 10-9. In addition, the error-floor level originating from the uncoded system is suppressed.