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A Comparative Review of Recent Advances in Decoding Algorithms for Low-Density Parity-Check (LDPC) Codes and Their Applications

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Abstract

In the domain of wireless communication systems, Error Control Coding (ECC) schemes are one of the widely relied upon or responsible methodology for securing the integrity and authenticity of the data transmission process. In the last decade, due to the advent of modern communication standards and their wide range of services, there has been a resurgence of interest and support in the research community towards the conception of efficient and versatile ECC techniques. Recent developments in the wireless communication based technologies have witnessed the pliable nature of low-density parity-check (LDPC) codes and their contributions which cannot be overstated. As of now, the decoding schemes based on LDPC codes have emerged as one of the most promising and effective coding scheme for addressing several key problems of reliable data communication. In this article, comprehensive overview on the current state-of-the art LDPC decoding algorithms and their applications are provided. In addition, a thorough investigation and comparison is carried out on various LDPC decoding algorithms based on their performance, similarities, scalability, numerical stability and feasibility for hardware realization. Finally, at the end of this review, views on the open research problems, challenges and the scope for future prospects are forecasted through discussions.

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References

  1. Huang L, Zhang H, Li R, Ge Y, Wang J (2020) AI coding: learning to construct error correction codes. IEEE Trans Commun 68(1):26–39

    Google Scholar 

  2. Xing Z, Liu K, Liu Y (2020) Low-complexity companding function design for PAPR reduction in OFDM systems. IET Commun 14(10):1581–1587

    Google Scholar 

  3. Arum SC, Grace D, Mitchell PD (2020) A review of wireless communication using high-altitude platforms for extended coverage and capacity. Comput Commun 157:232–256

    Google Scholar 

  4. Ye F, Dupraz E, Mheich Z, Amis K (2019) Optimized rate-adaptive protograph-based LDPC codes for source coding with side information. IEEE Trans Commun 67(6):3879–3889

    Google Scholar 

  5. Babar Z, Chandra D, Nguyen HV, Botsinis P, Alanis D, Ng SX, Hanzo L (2019) Duality of quantum and classical error correction codes: design principles and examples. IEEE Communications Surveys & Tutorials 21(1):970–1010

    Google Scholar 

  6. Egilmez ZBK, Xiang L, Maunder RG, Hanzo L (2020) The development, operation and performance of the 5G polar codes. IEEE Commun Surv Tutorials 22(1):96–122

    Google Scholar 

  7. Abdessalem MB, Zribi A, Matsumoto T, Dupraz E, Bouallègue A (2020) LDPC-based joint source channel coding and decoding strategies for single relay cooperative communications. Phys Commun 38:100947

    Google Scholar 

  8. Gallager RG (1962) Low-density parity-check codes. IRE Trans Inf Theory 8(1):21–28

    MathSciNet  MATH  Google Scholar 

  9. Mackay DJC (1999) Good error correcting codes based on very sparse matrices. IEEE Trans Inf Theory 45(2):399–431

    MathSciNet  MATH  Google Scholar 

  10. Davey MC, MacKay D (1998) Low-density parity check codes over GF(q). IEEE Commun Lett 2(6):165–167

    Google Scholar 

  11. Richardson TJ, Urbanke RL (2003) The Renaissance of Gallager’s low- density parity-check codes. IEEE Commun Mag 41(8):126–131

    Google Scholar 

  12. Roberts MK, Mohanram SS, Shanmugasundaram N (2019) An improved low complex offset min-sum based decoding algorithm for LDPC codes. Mobile Netw Appl 24(6):1848–1852

    Google Scholar 

  13. Chen Y, Cui H, Lin J, Wang Z (2020) Fine-grained bit-flipping decoding for LDPC codes. IEEE Trans Circuits Syst II Express Briefs 67(5):896–900

    Google Scholar 

  14. Zhang Z, Zhang K, Peng Z, Zeng D, Dai M (2020) Velocity analysis of BP decoding waves for SC-LDPC ensembles on BMS channels: an interpolation-based approach. IEEE Trans Commun 68(6):3286–3301

    Google Scholar 

  15. Delomier Y, Le Gal B, Crenne J, Jego C (2020) Model-based design of flexible and efficient LDPC decoders on FPGA devices. J Signal Process Syst 92(7):727–745

    Google Scholar 

  16. Lopez H, Chan H-W, Chiu K-L, Tsai P-Y, Jou S-JJ (2020) A 75-Gb/s/mm2 and energy-efficient LDPC decoder based on a reduced complexity second minimum approximation min-sum algorithm. IEEE Trans Very Large Scale Integr Syst 28(4):926–939

    Google Scholar 

  17. Li Q, Shi L, Di Y, Gao C, Ji C, Liang Y, Xue CJ (2020) Process variation aware read performance improvement for LDPC-based nand flash memory. IEEE Trans Reliab 69(1):310–321

    Google Scholar 

  18. Bonello N, Chen S, Hanzo L (2011) Low-density parity-check codes and their rateless relatives. IEEE Commun Surv Tutorials 13(1):3–26

    Google Scholar 

  19. Wang Z, Cui Z, Sha J (2011) VLSI design for low-density parity-check code decoding. IEEE Circuits Syst Mag 11(1):52–69

    Google Scholar 

  20. Ankan E, Hassan NU, Lentmaier M, Montorsi G, Sayir J (2015) Challenges and some new directions in channel coding. J Commun Netw 17(4):328–338

    Google Scholar 

  21. Andrade J, Falcao G, Silva V, Sousa L (2016) A survey on programmable LDPC decoders. IEEE Access 4:6704–6718

    Google Scholar 

  22. Fang Y, Bi G, Guan YL, Lau FCM (2015) A survey on protograph LDPC codes and their applications. IEEE Commun Surv Tutorials 17(4):1989–2016

    Google Scholar 

  23. Hailes P, Xu L, Maunder RG, Al-Hashimi BM, Hanzo L (2016) A survey of FPGA-based LDPC decoders. IEEE Commun Surv Tutorials 18(2):1098–1122

    Google Scholar 

  24. Fang Y, Han G, Cai G, Lau FCM, Chen P, Guan YL (2018) Design guidelines of low-density parity-check codes for magnetic recording systems. IEEE Commun Surv Tutorials 20(2):1574–1606

    Google Scholar 

  25. Shao S, Hailes P, Wang T-Y, Wu J-Y, Maunder RG, Al-Hashimi BM, Hanzo L (2019) Survey of turbo, LDPC, and polar decoder ASIC implementations. IEEE Commun Surv Tutorials 21(3):2309–2333

    Google Scholar 

  26. Tzimpragos G, Kachris C, Djordjevic IB, Cvijetic M, Soudris D, Tomkos I (2016) A survey on FEC codes for 100 G and beyond optical networks. IEEE Commun Surv Tutorials 18(1):209–221

    Google Scholar 

  27. Arora K, Singh J, Randhawa YS (2019) A survey on channel coding techniques for 5G wireless networks. Telecommun Syst 73(4):637–663

    Google Scholar 

  28. Roberts MK (2019) Simulation and implementation design of multi-mode decoder for WiMAX and WLAN applications. Measurement 131:28–34

    Google Scholar 

  29. Nguyen TTB, Lee H (2019) Low-complexity multi-mode multi-way split-row layered LDPC decoder for gigabit wireless communications. Integration 65:189–200

    Google Scholar 

  30. Ahn S-K, Kim K-J, Myung S, Park S-I, Yang K (2019) Comparison of low-density parity-check codes in ATSC 3.0 and 5G standards. IEEE Trans Broadcast 65(3):489–495

    Google Scholar 

  31. Zhang Y, Peng K, Wang X, Song J (2018) Performance analysis and code optimization of IDMA with 5G new radio LDPC code. IEEE Commun Lett 22(8):1552–1555

    Google Scholar 

  32. Awais M, Razzaq A, Ahmed A, Masera G (2019) LDPC check node implementation using reversible logic. IET Circuits Dev Syst 13(4):443–455

    Google Scholar 

  33. Xie Q, Sun Q (2019) Computation and application of robust data-driven bandwidth selection for gradient function estimation. Appl Math Comput 361(10):274–293

    MathSciNet  MATH  Google Scholar 

  34. Dai J, Zhou L, Chang C, Xu W (2020) Robust Bayesian learning approach for massive MIMO channel estimation. Sig Process 168(3):1–9

    Google Scholar 

  35. Xu H, Li H, Xu M, Feng D, Zhu H (2019) Two classes of QC-LDPC cycle codes approaching Gallager lower bound. Sci China Inf Sci 62:10

    MathSciNet  Google Scholar 

  36. Nishikawa M, Nakamura Y, Kanai Y, Osawa H, Okamoto Y (2019) A study on iterative decoding with LLR modulator by neural network using adjacent track information in SMR system. IEEE Trans Magn 55(12):1–5

    Google Scholar 

  37. Nguyen DT, Park Y (2019) Performance analysis of interleaved LDPC for optical satellite communications. Opt Commun 442(7):13–18

    Google Scholar 

  38. Mei Z, Cai K, Song G (2019) Performance analysis of finite-length LDPC codes over asymmetric memoryless channels. IEEE Trans Veh Technol 68(11):11338–11342

    Google Scholar 

  39. Boncalo O, Kolumban-Antal G, Declercq D, Savin V (2018) Code-design for efficient pipelined layered LDPC decoders with bank memory organization. Microprocess Microsyst 63(11):216–225

    Google Scholar 

  40. Elkelesh A, Ebada M, Cammerer S, Schmalen L, Brink ST (2019) Decoder-in-the-loop: genetic optimization-based LDPC code design. IEEE Access 7:141161–141170

    Google Scholar 

  41. Branco P, Mateus P, Salema C, Souto A (2020) Using low-density parity-check codes to improve the McEliece cryptosystem. Inf Sci 510(2):243–255

    MathSciNet  MATH  Google Scholar 

  42. Lee JH, Sunwoo MH (2019) Low-complexity high-throughput bit-wise LDPC decoder. J Signal Process Syst 91(8):855–862

    Google Scholar 

  43. Liu X, Xiong F, Wang Z, Liang S (2018) Design of binary LDPC codes with parallel vector message passing. IEEE Trans Commun 66(4):1363–1375

    Google Scholar 

  44. Català-Pérez JM, Lacruz JO, García-Herrero F, Valls J, Declercq D (2019) Second minimum approximation for min-sum decoders suitable for high-rate LDPC codes. Circuits Syst Signal Process 38(11):5068–5080

    Google Scholar 

  45. Li A, Meghdadi V, Cances J-P, Aupetit-Berthelemot C (2019) High-throughput 2 bit low-density parity-check forward error correction for C-RAN optical fronthaul based on a hard-decision algorithm. IET Circuits Dev Syst 13(2):111–116

    Google Scholar 

  46. Mondal A, Thatimattala S, Yalamaddi VK, Garani SS (2018) Efficient coding architectures for reed-solomon and low-density parity-check decoders for magnetic and other data storage systems. IEEE Trans Magn 54(2):1–15

    Google Scholar 

  47. Pradhan AK, Thangaraj A (2018) Protograph LDPC codes with block thresholds: extension to degree-one and generalized nodes. IEEE Trans Commun 66(12):5876–5887

    Google Scholar 

  48. Pramanik A, Maity SP, Sarkar S (2018) Compressed sensing image reconstruction by low density parity check codes and soft decoding of space time block codes. Comput Electr Eng 72(11):553–565

    Google Scholar 

  49. Mishra M (2019) LDPC codes and digital forensics—a perspective approach. IETE J Res 19:1–8

    Google Scholar 

  50. Gupta RS, Kamal TS, Singh PS (2019) Concatenated LDPC-TCM codes for better performance of OFDM-FSO system using gamma-gamma fading model. Wireless Pers Commun 106(4):2247–2260

    Google Scholar 

  51. Singh J, Gupta M, Bhullar JS (2019) Construction of girth-8 (3, L)-QC-LDPC codes of smallest CPM size using column multipliers. Des Codes Crypt 88(1):1–9

    MathSciNet  MATH  Google Scholar 

  52. Aswathy GP, Nair GK, Ahamed TPI (2019) Parallel concatenated Gallager codes for reliable data transmission in cognitive radio networks. Phys Commun 37(12):1–14

    Google Scholar 

  53. Yatribi A, Belkasmi M, Ayoub F (2020) Gradient-descent decoding of one-step majority-logic decodable codes. Phys Commun 39:100999

    Google Scholar 

  54. Kabakulak B, Taşkin ZC, Pusane AE (2019) A branch-and-cut algorithm for a bipartite graph construction problem in digital communication systems. Networks 75(2):137–157

    MathSciNet  Google Scholar 

  55. Gallager RG (1963) Low-density parity-check codes. MIT Press, Cambridge

    MATH  Google Scholar 

  56. Fossorier MPC, Mihaljevic M, Imai H (1999) Reduced complexity iterative decoding of low-density parity check codes based on belief propagation. IEEE Trans Commun 47(5):673–680

    Google Scholar 

  57. Kou Y, Lin S, Fossorier MPC (2001) Low-density parity-check codes based on finite geometries: a rediscovery and new results. IEEE Trans Inf Theory 47(7):2711–2736

    MathSciNet  MATH  Google Scholar 

  58. Zhang J, Fossorier MPC (2004) A modified weighted bit-flipping decoding of low-density parity-check codes. IEEE Commun Lett 8(3):165–167

    Google Scholar 

  59. Jiang M, Zhao C, Shi Z, Chen Yu (2005) An improvement on the modified weighted bit flipping decoding algorithm for LDPC codes. IEEE Commun Lett 9(9):814–816

    Google Scholar 

  60. Guo F, Hanzo L (2004) Reliability ratio based weighted bit-flipping decoding for low-density parity-check codes. Electron Lett 40(21):1356–1358

    Google Scholar 

  61. Lee C-H, Wolf W (2005) Implementation-efficient reliability ratio based weighted bit-flipping decoding for LDPC codes. Electron Lett 41(13):755–757

    Google Scholar 

  62. Chen T-C (2012) Channel-independent weighted bit-flipping decoding algorithm for low-density parity-check codes. IET Commun 6(17):2968–2973

    MathSciNet  MATH  Google Scholar 

  63. Zhang G, Zhou L, Wen H (2014) Modified channel-independent weighted bit flipping decoding algorithm for low-density-parity-check codes. IET Commun 8(6):833–840

    Google Scholar 

  64. Huang H, Wang Y, Wei G (2015) Mixed modified weighted bit-flipping decoding of low-density parity-check codes. IET Commun 9(2):283–290

    Google Scholar 

  65. Ismail M, Coon J, Ahmed I, Armour S, McGeehan J (2013) Turbo adaptive threshold bit flipping for LDPC decoding. IEEE Wireless Commun Lett 2(1):118–121

    Google Scholar 

  66. Chen T-C (2013) Adaptive-weighted multibit-flipping decoding of low-density parity-check codes based on ordered statistics. IET Commun 7(14):1517–1521

    Google Scholar 

  67. Tiwari HD, Tiwari HD, Lee K-Y (2014) Hybrid weighted bit flipping low density parity check decoding. Digit Signal Proc 28:82–92

    Google Scholar 

  68. Ma K, Li Y, Zhu C, Zhang H, Zhang Y (2014) Lowering error floor of LDPC codes using an improved parallel WBF algorithm. ETRI J 36(1):171–174

    Google Scholar 

  69. Nguyen DV, Vasic B (2014) Two-bit bit flipping algorithms for LDPC codes and collective error correction. IEEE Trans Commun 62(4):1153–1163

    Google Scholar 

  70. Roberts MK, Jayabalan R (2014) An improved low complex hybrid weighted bit-flipping algorithm for LDPC codes. Wireless Pers Commun 82(1):327–339

    Google Scholar 

  71. Hatami H, Mitchell DGM, Costello DJ, Fuja TE (2020) A threshold-based min-sum algorithm to lower the error floors of quantized LDPC decoders. IEEE Trans Commun 68(4):2005–2015

    Google Scholar 

  72. Liu Y, Niu X, Zhang M (2015) Multi-threshold bit flipping algorithm for decoding structured LDPC codes. IEEE Commun Lett 19(2):127–130

    Google Scholar 

  73. Chang TC-Y, Su YT (2015) Dynamic weighted bit-flipping decoding algorithms for LDPC codes. IEEE Trans Commun 63(11):3950–3963

    Google Scholar 

  74. Elsanadily S, Mahran A, Elghandour O (2017) Two-side state-aided bit-flipping decoding of generalized low density parity check codes. IEEE Commun Lett 21(10):2122–2125

    Google Scholar 

  75. Oh J, Ha J (2018) A two-bit weighted bit-flipping decoding algorithm for LDPC codes. IEEE Commun Lett 22(5):874–877

    Google Scholar 

  76. Wang Y, Wu G (2018) Cyclic switching weighted bit-flipping decoding for low-density parity-check codes. IET Commun 12(3):271–275

    Google Scholar 

  77. Le K, Ghaffari F, Kessal L, Declercq D, Boutillon E, Winstead C, Vasic B (2019) A probabilistic parallel bit-flipping decoder for low-density parity-check codes. IEEE Trans Circuits Syst I Regul Pap 66(1):403–416

    Google Scholar 

  78. Liu Y, Zhang M (2019) Hard-decision bit-flipping decoder based on adaptive bit-local threshold for LDPC codes. IEEE Commun Lett 23(5):789–792

    Google Scholar 

  79. Kalipatnapu S, Chakrabarti I (2019) High-throughput Bit Flipping decoder for structured LDPC codes. IET Commun 13(14):2168–2172

    Google Scholar 

  80. Chang TC-Y, Wang P-H, Su YT (2019) Multi-stage bit-flipping decoding algorithms for LDPC codes. IEEE Commun Lett 23(9):1524–1528

    Google Scholar 

  81. Chou H-F, Sham C-W (2018) An optimization approach for an RLL-constrained LDPC coded recording system using deliberate flipping. IEEE Commun Lett 22(10):1976–1979

    Google Scholar 

  82. Dai B, Liu R, Gao C, Mei Z (2019) Symbol flipping algorithm with self-adjustment strategy for LDPC codes over GF(q). IEEE Trans Veh Technol 68(7):7189–7193

    Google Scholar 

  83. Hu Y, Song S, Xiao S, Xu Q, Xiao N, Qin Z (2015) A dominating error region strategy for improving the bit-flipping LDPC decoder of SSDs. IEEE Trans Circuits Syst II Express Briefs 62(6):578–582

    Google Scholar 

  84. Liu Y-C, Chang C-F, Lee S-K, Lin M-C (2017) Deliberate bit flipping with error-correction for PAPR reduction. IEEE Trans Broadcast 63(1):123–133

    Google Scholar 

  85. Jung N, Park I-C (2017) Multi-bit flipping decoding of LDPC codes for NAND storage systems. IEEE Commun Lett 21(5):979–982

    Google Scholar 

  86. Sohrabi MK, Azgomi H (2018) A survey on the combined use of optimization methods and game theory. Arch Comput Methods Eng 27(1):59–80

    MathSciNet  Google Scholar 

  87. Zhang Y, Li Q, Huang L, Dai K, Song J (2018) Optimal design of cascade LDPC-CPM system based on bionic swarm optimization algorithm. IEEE Trans Broadcast 64(3):762–770

    Google Scholar 

  88. Rojc M, Mlakar I (2020) A new fuzzy unit selection cost function optimized by relaxed gradient descent algorithm. Expert Syst Appl 159:113552

    Google Scholar 

  89. Wadayama T, Nakamura K, Yagita M, Funahashi Y, Usami S, Takumi I (2010) Gradient descent bit flipping algorithms for decoding LDPC codes. IEEE Trans Commun 58(6):1610–1614

    Google Scholar 

  90. Nakamura K, Wadayama T, Yagita M, Funahashi Y, Usami S, Takumi I (2008) Improved gradient descent-bit flipping decoding using multi thresholds. In: Proceedings of the IEICE general conference, pp 160 (in Japanese)

  91. Asatani J, Kawanishi H, Tokushige H, Katayama K (2015) Frequency memory based gradient descent bit flipping algorithm. IEE J Trans Electr Electron Eng 10(5):585–591

    Google Scholar 

  92. Sundararajan G, Winstead C, Boutillon E (2014) Noisy gradient descent bit-flip decoding for LDPC codes. IEEE Trans Commun 62(10):3385–3400

    Google Scholar 

  93. Rasheed OA, Ivanis P, Vasic B (2014) Fault-tolerant probabilistic gradient-descent bit flipping decoder. IEEE Commun Lett 18(9):1487–1490

    Google Scholar 

  94. Le K, Ghaffari F, Declercq D, Vasic B (2017) Efficient hardware implementation of probabilistic gradient descent bit-flipping. IEEE Trans Circuits Syst I Regul Pap 64(4):906–917

    Google Scholar 

  95. Ren D, Sha J (2018) Improved gradient descent bit flipping decoder for LDPC codes on BSC channel. IEICE Electron Express 15(8):20180195–20180195

    Google Scholar 

  96. Li H, Ding H, Zheng L (2017) Modified gradient descent bit-flipping decoding for low-density parity-check codes. Wireless Pers Commun 96(4):6459–6472

    Google Scholar 

  97. Dai B, Liu R, Gao C, Mei Z (2018) Noisy gradient descent bit-flipping decoder based on adjustment factor for LDPC codes. IEEE Commun Lett 22(6):1152–1155

    Google Scholar 

  98. Cui H, Lin J, Wang Z (2019) An improved gradient descent bit-flipping decoder for LDPC codes. IEEE Trans Circuits Syst I Regul Pap 66(8):3188–3200

    Google Scholar 

  99. Unal B, Akoglu A, Ghaffari F, Vasic B (2018) Hardware implementation and performance analysis of resource efficient probabilistic hard decision LDPC decoders. IEEE Trans Circuits Syst I Regul Pap 65(9):3074–3084

    Google Scholar 

  100. Ueng Y-L, Wang C-Y, Li M-R (2017) An efficient combined bit-flipping and stochastic LDPC decoder using improved probability tracers. IEEE Trans Signal Process 65(20):5368–5380

    MathSciNet  MATH  Google Scholar 

  101. Rao RV, Saroj A, Ocloń P, Taler J (2019) Design optimization of heat exchangers with advanced optimization techniques: a review. Arch Comput Methods Eng 27(2):517–548

    Google Scholar 

  102. Zhang J, Peng Y, Ouyang W, Deng B (2019) Accelerating ADMM for efficient simulation and optimization. ACM Trans Graph 38(6):1–21

    Google Scholar 

  103. Xiu X, Liu W, Li L, Kong L (2019) Alternating direction method of multipliers for nonconvex fused regression problems. Comput Stat Data Anal 136:59–71

    MathSciNet  MATH  Google Scholar 

  104. Falsone A, Notarnicola I, Notarstefano G, Prandini M (2020) Tracking-ADMM for distributed constraint-coupled optimization. Automatica 117:108962

    MathSciNet  MATH  Google Scholar 

  105. Jian L, Hu J, Wang J, Shi K (2019) Distributed inexact dual consensus ADMM for network resource allocation. Optimal Control Appl Methods 40(6):1071–1087

    MathSciNet  MATH  Google Scholar 

  106. Vargas H, Ramirez J, Arguello H (2020) ADMM-based ℓ1−ℓ1 optimization algorithm for robust sparse channel estimation in OFDM systems. Signal Process 167:107296

    Google Scholar 

  107. Bao H, Fang J, Wan Q, Chen Z, Jiang T (2018) An ADMM approach for PAPR reduction for large-scale MIMO-OFDM systems. IEEE Trans Veh Technol 67(8):7407–7418

    Google Scholar 

  108. Wang Y, Wang Y, Shi Q (2019) Optimized signal distortion for PAPR reduction of OFDM signals with IFFT/FFT complexity via ADMM approaches. IEEE Trans Signal Process 67(2):399–414

    MathSciNet  MATH  Google Scholar 

  109. Chen J, Fossorier M (2002) Density evolution for two improved BP-based decoding algorithms of LDPC codes. IEEE Commun Lett 6(5):208–210

    Google Scholar 

  110. Kschischang FR, Frey BJ, Loeliger HJ (2001) Factor graphs and Sum-product algorithm. IEEE Trans Inf Theory 47(2):498–519

    MathSciNet  MATH  Google Scholar 

  111. Oh D, Parhi KK (2010) Min-sum decoder architectures with reduced word length for LDPC codes. IEEE Trans Circuits Syst I Regular Pap 57(1):105–115

    MathSciNet  Google Scholar 

  112. Mansour MM, Shanbhag NR (2003) High-throughput LDPC decoders. IEEE Trans Very Large Scale Integr Syst 11(6):976–996

    Google Scholar 

  113. Jiang M, Zhao C, Zhang L, Enyang X (2006) Adaptive offset min-sum algorithm for low-density parity check codes. IEEE Commun Lett 10(6):483–485

    Google Scholar 

  114. Wei H, Jiao X, Mu J (2015) Reduced-complexity linear programming decoding based on ADMM for LDPC codes. IEEE Commun Lett 19(6):909–912

    Google Scholar 

  115. Jiao X, Wei H, Mu J, Chen C (2015) Improved ADMM penalized decoder for irregular low-density parity-check codes. IEEE Commun Lett 19(6):913–916

    Google Scholar 

  116. Storn R, Price K (1997) Differential evolution: a simple and efficient heuristic for global optimization over continuous spaces. J Global Optim 11(4):341–359

    MathSciNet  MATH  Google Scholar 

  117. Debbabi I, Gal BL, Khouja N, Tlili F, Jego C (2016) Fast converging ADMM-penalized algorithm for LDPC decoding. IEEE Commun Lett 20(4):648–651

    Google Scholar 

  118. Barman S, Liu X, Draper SC, Recht B (2013) Decomposition methods for large scale LP decoding. IEEE Trans Inf Theory 59(12):7870–7886

    MathSciNet  MATH  Google Scholar 

  119. Liu X, Draper SC (2016) The ADMM penalized decoder for LDPC codes. IEEE Trans Inf Theory 62(6):2966–2984

    MathSciNet  MATH  Google Scholar 

  120. Jiao X, Mu J (2016) Lowering the error floor of ADMM penalized decoder for LDPC codes. China Commun 13(8):127–135

    Google Scholar 

  121. Debbabi I, Le Gal B, Khouja N, Tlili F, Jego C (2016) Real time LP decoding of LDPC codes for high correction performance applications. IEEE Wireless Commun Lett 5(6):676–679

    Google Scholar 

  122. Yu L, Lin N (2017) ADMM for penalized quantile regression in big data. Int Stat Rev 85(3):494–518

    MathSciNet  Google Scholar 

  123. Wang B, Mu J, Jiao X, Wang Z (2017) Improved penalty functions of ADMM penalized decoder for LDPC codes. IEEE Commun Lett 21(2):234–237

    Google Scholar 

  124. Jiao X, Mu J, Wei H (2017) Reduced complexity node-wise scheduling of ADMM decoding for LDPC codes. IEEE Commun Lett 21(3):472–475

    Google Scholar 

  125. Casado AIV, Griot M, Wesel RD (2010) LDPC decoders with informed dynamic scheduling. IEEE Trans Commun 58(12):3470–3479

    Google Scholar 

  126. Lee H-C, Ueng Y-L, Yeh S-M, Weng W-Y (2013) Two informed dynamic scheduling strategies for iterative LDPC decoders. IEEE Trans Commun 61(3):886–896

    Google Scholar 

  127. Liu X, Zhou Z, Cui R, Liu E (2016) Informed decoding algorithms of LDPC codes based on dynamic selection strategy. IEEE Trans Commun 64(4):1357–1366

    Google Scholar 

  128. Tehrani SS, Mannor S, Gross WJ (2008) Fully parallel stochastic LDPC decoders. IEEE Trans Signal Process 56(11):5692–5703

    MathSciNet  MATH  Google Scholar 

  129. Jiao X, Mu J, He Y-C, Chen C (2017) Efficient ADMM decoding of LDPC codes using lookup tables. IEEE Trans Commun 65(4):1425–1437

    Google Scholar 

  130. Khittiwitchayakul S, Phakphisut W, Supnithi P (2018) Reduced complexity window decoding of spatially coupled LDPC codes for magnetic recording systems. IEEE Trans Magn 54(11):1–5

    Google Scholar 

  131. Jiao X, He Y-C, Mu J (2018) Memory-reduced look-up tables for efficient ADMM decoding of LDPC codes. IEEE Signal Process Lett 25(1):110–114

    Google Scholar 

  132. Zhang Q, Wang M, Lu Y, Zhang L, Idrees M (2019) A novel fast nonstationary noise tracking approach based on MMSE spectral power estimator. Digital Signal Proc 88:41–52

    Google Scholar 

  133. Wei H, Banihashemi AH (2018) An iterative check polytope projection algorithm for ADMM-based LP decoding of LDPC codes. IEEE Commun Lett 22(1):29–32

    Google Scholar 

  134. Wu Q, Zhang F, Wang H, Lin J, Liu Y (2018) Parameter-free lp-box decoding of LDPC codes. IEEE Commun Lett 22(7):1318–1321

    Google Scholar 

  135. Wu B, Ghanem B (2019) Lp-box ADMM: a versatile framework for integer programming. IEEE Trans Pattern Anal Mach Intell 41(7):1695–1708

    Google Scholar 

  136. Bai J, Wang Y, Lau FCM (2019) Minimum-polytope-based linear programming decoder for LDPC codes via ADMM approach. IEEE Wireless Commun Lett 8(4):1032–1035

    Google Scholar 

  137. Xia Q, Lin Y, Tang S, Zhang Q (2019) A fast approximate check polytope projection algorithm for ADMM decoding of LDPC codes. IEEE Commun Lett 23(9):1520–1523

    Google Scholar 

  138. Bai J, Wang Y, Shi Q (2020) Efficient QP-ADMM decoder for binary LDPC codes and its performance analysis. IEEE Trans Signal Process 68:503–518

    MathSciNet  Google Scholar 

  139. Wang B, Wang Z (2020) ADMM penalized decoding method based on improved penalty function for LDPC codes in the IoTs. Comput Commun 154:197–203

    Google Scholar 

  140. Wei Y, Zhao M-M, Zhao M-J, Lei M (2020) ADMM-based decoder for binary linear codes aided by deep learning. IEEE Commun Lett 24(5):1028–1032

    Google Scholar 

Download references

Funding

This research work is funded by the Department of Science and Technology, Government of INDIA through Early Career Research Award (Young Scientist) scheme of Science and Engineering Research Board (SERB) (Grant No. ECR/2016/001275).

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  1. Department of Electronics and Communication Engineering, Sri Eshwar College of Engineering, Coimbatore, 641202, Tamil Nadu, India

    Michaelraj Kingston Roberts & Anguraj Parthibaraj

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  1. Michaelraj Kingston Roberts
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  2. Anguraj Parthibaraj
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Correspondence to Michaelraj Kingston Roberts.

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Roberts, M.K., Anguraj, P. A Comparative Review of Recent Advances in Decoding Algorithms for Low-Density Parity-Check (LDPC) Codes and Their Applications. Arch Computat Methods Eng 28, 2225–2251 (2021). https://doi.org/10.1007/s11831-020-09466-6

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