A Construction of High Performance Quasicyclic LDPC Codes: A Combinatoric Design Approach

Asif, Muhammad; Zhou, Wuyang; Ajmal, Muhammad; Akhtar, Zain Ul Abiden; Khan, Nauman Ali

doi:10.1155/2019/7468792

Cited by 11 publications

(16 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Figure 6 shows the BER performance of the proposed jointly designed QC-LDPC code Wireless Communications and Mobile Computing 9 C (4) qc and the QC-LDPC-coded cooperation [39] under different decoding iterations. Simulation results show that the error correcting performance of the QC-LDPC-coded cooperation [39] is inferior than the proposed jointly designed QC-LDPC-coded cooperation under the same conditions over a Rayleigh fading channel in the presence of additive white Gaussian noise. For instance, at BER 10 − 6 , jointly designed coded-relay cooperation provides a gain of about 0.6 dB with 4 decoding iterations.…”

Section: Jointly Designed Qc-ldpc-coded Cooperation Based Onmentioning

confidence: 99%

“…For instance, at BER 10 − 6 , jointly designed coded-relay cooperation provides a gain of about 0.6 dB with 4 decoding iterations. e relevant parameters for component QC-LDPC codes adopted for C (4) qc and QC-LDPC-coded cooperation [39] are given in Table 3, where the overall code rate is 1/2 from the destination.…”

Section: Jointly Designed Qc-ldpc-coded Cooperation Based Onmentioning

confidence: 99%

“…eoretical analysis and simulation results show that the proposed jointly designed QC-LDPC coded-relay cooperations outperform their counterparts under the same conditions over a Rayleigh-fading channel in the presence of additive white Gaussian noise. Coded cooperation [39], iteration = 3…”

Section: Conclusion and Remarksmentioning

confidence: 99%

“…Coded cooperation [39], iteration = 4 Figure 6: Error correcting performance of the proposed jointly designed QC-LDPC coded-relay cooperation and QC-LDPC coded-relay cooperation cooperation [39] over a Rayleigh fading channel in the presence of additive white Gaussian noise.…”

Section: Conclusion and Remarksmentioning

confidence: 99%

“…If a parity-check matrix composed of an array of circulant permutation matrices, then its null space gives a QC-LDPC code over a finite field GF(ρ) [23][24][25]. If a parity-check matrix satisfies a constraint that no two rows or columns can overlap, in terms of a nonzero element, at more than one positions, then this constraint is known as row-column-(RC-) constraint which ensures that the Tanner graph representation of H has a girth of at least 6. e construction spectrum of LDPC codes is divided into two categories: (A) computer-based LDPC codes are constructed based on random construction methods, PEG-LDPC [26] codes are considered as one of the most promising random-LDPC codes, and protographbased [27] techniques; (B) structured-LDPC (e.g., QC-LDPC) codes are obtained from deterministic or algebraic techniques such as finite fields [23,24,[28][29][30], finite geometries [31,32], and combinatorial designs [33][34][35][36][37][38][39][40]. Quasicyclic or architecture-aware LDPC codes have been adopted by many communication standards because of their efficient architecture which reduces computational cost of an encoder and decoder.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

A Deterministic Construction for Jointly Designed Quasicyclic LDPC Coded-Relay Cooperation

Asif

Zhou

et al. 2019

Wireless Communications and Mobile Computing

Self Cite

View full text Add to dashboard Cite

This correspondence presents a jointly designed quasicyclic (QC) low-density parity-check (LDPC) coded-relay cooperation with joint-iterative decoding in the destination node. Firstly, a design-theoretic construction of QC-LDPC codes based on a combinatoric design approach known as optical orthogonal codes (OOC) is presented. Proposed OOC-based construction gives three classes of binary QC-LDPC codes with no length-4 cycles by utilizing some known ingredients including binary matrix dispersion of elements of finite field, incidence matrices, and circulant decomposition. Secondly, the proposed OOC-based construction gives an effective method to jointly design length-4 cycles free QC-LDPC codes for coded-relay cooperation, where sum-product algorithm- (SPA-) based joint-iterative decoding is used to decode the corrupted sequences coming from the source or relay nodes in different time frames over constituent Rayleigh fading channels. Based on the theoretical analysis and simulation results, proposed QC-LDPC coded-relay cooperations outperform their competitors under same conditions over the Rayleigh fading channel with additive white Gaussian noise.

show abstract

Section: Jointly Designed Qc-ldpc-coded Cooperation Based Onmentioning

confidence: 99%

Section: Jointly Designed Qc-ldpc-coded Cooperation Based Onmentioning

confidence: 99%

Section: Conclusion and Remarksmentioning

confidence: 99%

Section: Conclusion and Remarksmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A Deterministic Construction for Jointly Designed Quasicyclic LDPC Coded-Relay Cooperation

Asif

Zhou

et al. 2019

Wireless Communications and Mobile Computing

Self Cite

View full text Add to dashboard Cite

show abstract

Network coding schemes with efficient LDPC coded MIMO–NOMA in two‐way relay networks

et al. 2020

View full text Add to dashboard Cite

The combination of non-orthogonal multiple access (NOMA) and multi-input multi-output (MIMO) approaches has been considered as assuring multiple access for the fifth generation technology. In this study, the performance of a 2 × 2 MIMO-NOMA system with low-density parity check (LDPC) codes is investigated. Redundancy with randomly interleaved differential encoding (R-RIDE) is proposed and applied to LDPC encoded messages by two users. LDPC decoding is done using the sum-product algorithm (SPA), which has two types of decoding methods, hard-decision and soft-decision. For hard-decision, bit-flipping decoder is used and for soft-decision, probability domain, log-domain, and simplified log-domain decoders are used. Bit error rate (BER) versus signal-to-noise ratio (SNR) in (dB) and average mutual information (AMI) in (bps/Hz) versus SNR (dB) are evaluated to compare the performance of the proposed and conventional LDPC schemes in NOMA and MIMO-NOMA systems. Simulation results show that both AMI and BER of the proposed LDPC-R-RIDE in MIMO-NOMA system greatly outperforms conventional LDPC coded schemes in NOMA and MIMO-NOMA systems. Moreover, the proposed R-RIDE-LDPC in MIMO-NOMA system outperforms the proposed scheme in the NOMA system. From the simulation results, LDPC-R-RIDE with simplified log-domain decoder has the best AMI result and BER performance compared with other decoding methods.

show abstract

A Note on the Girth of (3, 19)-Regular Tanner’s Quasi-Cyclic LDPC Codes

Zhou

Zhu

et al. 2021

IEEE Access

View full text Add to dashboard Cite

In this paper, we study the cycle structure of (3, 19)-regular Tanner's quasi-cyclic (QC) LDPC codes with code length 19p, where p is a prime and p ≡ 1 (mod 57), and transform the conditions for the existence of cycles of lengths not more than 10 into polynomial equations in a 57th root of unity of the prime field F p. By employing the Euclidean division algorithm to check whether these equations have solutions over the prime field F p , the girth values of (3, 19)-regular Tanner's QC-LDPC codes of code length 19p are determined. In order to show the good performance of this class of QC-LDPC codes, numerical results are also provided. INDEX TERMS QC-LDPC codes, Tanner graph, girth, prime field I. INTRODUCTION Quasi-cyclic (QC) LDPC codes [1] are a class of wellknown channel codes, and widely used in the communication and storage systems because of their excellent features: lowcomplexity encoding and decoding algorithms [2]-[5], good performance in the waterfall and error-floor regions [6]-[10], and easy implementations in hardware [11]-[13]. In general, the low-complexity algorithms for decoding LDPC codes are under the frame of iterative decoding. However, short cycles in the Tanner graph [14] of an LDPC code degrade the iterative decoding performance. Hence, constructing large girth LDPC codes and/or determining their girths is of interest in coding theory and graph theory [15], [16].

show abstract

A Construction of High Performance Quasicyclic LDPC Codes: A Combinatoric Design Approach

Cited by 11 publications

References 38 publications

A Deterministic Construction for Jointly Designed Quasicyclic LDPC Coded-Relay Cooperation

A Deterministic Construction for Jointly Designed Quasicyclic LDPC Coded-Relay Cooperation

Network coding schemes with efficient LDPC coded MIMO–NOMA in two‐way relay networks

A Note on the Girth of (3, 19)-Regular Tanner’s Quasi-Cyclic LDPC Codes

Contact Info

Product

Resources

About