Skip to main content

Advertisement

Log in

A survey on channel coding techniques for 5G wireless networks

  • Published:
Telecommunication Systems Aims and scope Submit manuscript

Abstract

Although 4G (fourth generation) i.e. LTE (long term evolution) systems are now in use world-wide. But today’s 4G systems have some challenges left such as spectrum scarcity and energy efficiency. The prime objectives of near-by-future 5G (fifth generation) wireless communications are reliability, higher data rate, higher bandwidth, high spectrum efficiency, higher energy efficient and that too at lower latency. Channel coding tend to increase the reliability of the wireless communications system by adding extra bits in a controlled fashion and is considered to be most persuasive element of communication system. 4G LTE Turbo Codes have already been replaced by LDPC (low density parity check) Codes in many of the standards including mMTC (massive machine type communication), D2D (device to device communication) and URLLC (ultra-reliable low latency reliable communications). LDPC Codes and Polar Codes are securing much more observation because of their inherent advantages of excellent bit-error-rate performance, fast encoding and decoding procedures; which make them the strong contenders for 5G Channel Codes too. This paper provides the broad survey and comparison of the LDPC and Polar Codes along with their advantages and drawbacks which will aid in further improvement of the next generation wireless networks. In order to enlighten future research possibilities in this direction, issues addressed by distinct researchers have been explored too.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Abbreviations

LTE:

Long term evolution

IoT:

Internet of things

LDPC:

Low density parity check

SNR:

Signal to noise ratio

FEC:

Forward error correction

mMTC:

Massive machine type communication

D2D:

Device to device communication

URLLC:

Ultra-reliable low latency reliable communications

AMPS:

Advanced mobile phone systems

NTT:

Nippon telegraph and telephone

TACS:

Total access communications system

IS-95:

Interim standard 95

PDC:

Pacific digital cellular systems

GPRS:

General packet radio service

EDGE:

Enhanced data rate for GSM evolution

UMTS:

Universal mobile telecommunication systems

HSPA:

High speed packet access

CDMA:

code division multiple access

BSC:

Base station controller

RNC:

Radio network controller

TDMA:

Time division multiple access

GSM:

Global system for mobile

FDMA:

Frequency division multiple access

WCDMA:

Wideband code division multiple access

UMTS:

Universal mobile telecommunication system

HSPA:

High speed packet access

EvDO:

Evolution data optimized

QPSK:

Quadrature phase shift keying

OFDMA:

Orthogonal frequency division multiple access

SC-FDMA:

Single carrier frequency division multiple access

S-OFDMA:

Scalable orthogonal frequency division multiple access

BDMA:

Beam division multiple access

FBMC:

Filter bank multiple carrier multiple access

BCH:

Bose–Chaudhuri–Hocquenghem Codes

LT:

Luby transform codes

UWB:

Ultra wide band communications

SE:

Spectral efficiency

NBLC:

Non-binary LDPC codes

PCM:

Parity check matrix

BG:

Bi-partite graph

RLDPC:

Regular LDPC codes

IRLDPC:

Irregular LDPC Codes

CP:

Closed path

CG:

Connected graph

SG:

Sub graph

ISG:

Induces sub-graph

TC:

Trapping cycle

ETC:

Elementary trapped cycle

ML:

Maximum likelihood

LR:

Likelihood ratio

LLR:

Log likelihood ratio

AWGN:

Additive white Gaussian noise

BDC:

Binary discrete channels

SC:

Successive cancellation

SSC:

Simplified successive cancellation

LSC:

List successive cancellation

CRC:

Cyclic redundancy check

MPA:

Message passing algorithm

AMA:

Addition–multiplication algorithm

MS:

Min–sum algorithm

WB:

Weighted bit-flicking

BS:

Boot-strapping

WC:

Weighing-coefficient

QAMA:

Q-ary addition–multiplication algorithm

EMSA:

Elongated minimum–sum algorithm

TEMSA:

Trellis-based-EMSA

DP:

Deviation paths

FPMSA:

Fixed path minimum sum algorithm

GF:

Galois field

BER:

Bit error rate

RW:

Re-weighing

RS:

Re-scheduling

RBPA:

Residual-belief-propagation-algorithm

NBPA:

Node-wise-belief-propagation-algorithm

LBPA:

Layered-belief-propagation-algorithm

DSOC:

Deep Space optical communications

HSC:

Helicopter satellite communications

PPMBPC:

PPM based Poisson channel

QC-LDPC:

Quasi-cyclic LDPC Codes

MCS:

Mobile-satellite communication system

MIMO:

Multiple input multiple output

References

  1. Turjman, F. A. (2017). Cognitive caching for the future sensors in fog networking. Pervasive Mobile Computing,42, 317–334.

    Google Scholar 

  2. Salah, A. A., & Turjman, F. A. (2018). Low complexity parity check code for futuristic wireless networks applications. IEEE Access,6, 18398–18407.

    Google Scholar 

  3. Niu, K., Chen, K., Lin, J., & Zhang, Q. T. (2014). Polar codes: Primary concepts and practical decoding algorithms. IEEE Communications Magazine,52(7), 192–203.

    Google Scholar 

  4. Berrou, C., & Glavieux, A. (1996). Near optimum error correcting coding and decoding: Turbo-codes. IEEE Transactions on Communications,44, 1261–1271.

    Google Scholar 

  5. MacKay, D. J. C., & Neal, R. M. (1997). Near shannon limit performance of low density parity check codes. Electronics Letters,33, 457–458.

    Google Scholar 

  6. MacKay, D. J. C. (1999). Good error-correcting codes based on very sparse matrices. IEEE Transactions on Information Theory,45(2), 399–431.

    Google Scholar 

  7. Richardson, T., & Urbanke, R. (2001). The capacity of low-density parity-check codes under message-passing decoding. IEEE Transactions on Information Theory,47, 599–618.

    Google Scholar 

  8. Spielman, D. (1996). Linear-time encodable and decodable error-correcting codes. IEEE Transactions on Information Theory,42(6), 1723–1731.

    Google Scholar 

  9. Luby, M. G., Mitzenmacher, M., Shokrollahi, M. A., Spielman, D. A., & Stemann, V. (1997). Practical loss-resilient codes. In Proceedings of 29th annual ACM symposium on theory of computing (pp. 150–159).

  10. Richardson, T., & Urbanke, R. (2001). Efficient encoding of low-density parity-check codes. IEEE Transactions on Information Theory,47(2), 638–656.

    Google Scholar 

  11. Richardson, T., Shokrollahi, M., & Urbanke, R. (2001). Design of capacity approaching irregular low-density parity-check codes. IEEE Transactions on Information Theory,47(2), 619–637.

    Google Scholar 

  12. ten Brink, S. (2001). Convergence behavior of iteratively decoded parallel concatenated codes. IEEE Transactions on Communications,49(10), 1727–1737.

    Google Scholar 

  13. Brink, S., Kramer, G., & Ashikhmin, A. (2004). Design of low-density parity-check codes for modulation and detection. IEEE Transactions on Communications,52(4), 670–678.

    Google Scholar 

  14. Ashikhmin, A., Kramer, G., & Brink, S. (2004). Extrinsic information transfer functions: Model and erasure channel properties. IEEE Transactions on Information Theory,50(11), 2657–2673.

    Google Scholar 

  15. Prayogo, G. K., Putra, R., Prasetyo, A. H., & Suryanegara, M. (2018). A 5G new radio LDPC coded NOMA scheme supporting high user load for massive MTC. In International conference on information technology and electrical engineering (ICITEE) (pp. 170–174).

  16. Wu, X., Jiang, M., Zhao, C., Ma, L., & Wei, Y. (2018). Low-rate PBRL-LDPC codes for URLLC in 5G. IEEE Wireless Communications Letters.,7(5), 800–803.

    Google Scholar 

  17. Sharma, A, & Salim, M. (2017). Polar Code: The Channel Code contender for 5G scenarios. In International conference on computer, communications and electronics (Comptelix) (pp. 676–682).

  18. Wang, R., & Rongke, L. A. (2014). Novel puncturing scheme for polar codes. IEEE Communication on Letters,18(12), 2081–2083.

    Google Scholar 

  19. Arıkan, E. (2009). Channel polarization: A method for constructing capacity-achieving codes. IEEE Transactions on Information Theory,55(7), 3051–3073.

    Google Scholar 

  20. Marconi, G. (1899). Wireless telegraphy. Journal of the Institution of Electrical Engineers,28(139), 273–290.

    Google Scholar 

  21. Sofi, I. B., & Gupta, A. (2018). A survey on energy efficient 5G green network with a planned multi-tier architecture. Journal of Network and Computer Applications,118, 1–28.

    Google Scholar 

  22. Khan, F. (2009). LTE for 4G mobile broadband: Air interface technologies and performance. Cambridge: Cambridge University Press.

    Google Scholar 

  23. Khan, M. N., Gilani, S. O., Jamil, M., Rafay, A., et al. (2018). Maximizing throughput of hybrid FSO-RF communication system: An algorithm. IEEE Access,6, 30039–30048.

    Google Scholar 

  24. Yang, L., Xie, Y., Yuan, J., Cheng, X., & Wan, L. (2018). Chained LDPC codes for future communication systems. IEEE Communications Letters,22(5), 898–901.

    Google Scholar 

  25. Andrews, J. G., Buzzi, S., Choi, W., et al. (2014). What will 5G be. IEEE Journal on Selected Areas in Communications,32(6), 1065–1082.

    Google Scholar 

  26. Kong, L., Khan, M. K., Wu, F., Chen, G., & Zeng, P. (2017). Millimeter-wave wireless communications for IoT-cloud supported autonomous vehicles: Overview, design, and challenges. IEEE Communications Magazine,55(1), 62–68.

    Google Scholar 

  27. Liang, Z., Zang, J., Yang, X., Dong, X., & Song, H. (2017). Low-density parity-check codes for noncoherent UWB communication systems. China Communications,14(7), 1–11.

    Google Scholar 

  28. Hung-Ta, P., Han, Y. S., & Chu, Y. J. (2011). New HARQ scheme based on decoding of tail-biting convolutional codes in IEEE 802.16e. IEEE Transactions on Vehicular Technology,60(3), 912–918.

    Google Scholar 

  29. GPP TSG-RAN WG1 #86. (2016). Discussion on outer coding on eMBB data. LG Electronics.

  30. Peng, R. H., & Chen, R. R. (2006). Application of non-binary LDPC codes for communication over fading channels using higher order modulations. In Proceedings of IEEE global communications conference (GLOBECOM).

  31. Feng, D., Xu, H., Zheng, J., & Bai, B. (2018). Nonbinary LDPC-coded spatial modulation. IEEE Transactions on Wireless Communications,17(4), 2786–2799.

    Google Scholar 

  32. Chen, X., & Wang, C. L. (2012). High-throughput efficient non-binary LDPC decoder based on the simplified min-sum algorithm. IEEE Transactions on Circuits and Systems,59(11), 2784–2794.

    Google Scholar 

  33. Shannon, C. E.(1948). A mathematical theory of communication. Bell System Technical Journal, 27:379–423, 623–656.

    Google Scholar 

  34. Calderbank, A., & Mazo, J. (1984). A new description of trellis codes. IEEE Transactions on Information Theory,30(6), 784–791.

    Google Scholar 

  35. Lin, S., & Costello, D. J. (2004). Error control coding: Fundamentals and applications (2nd ed.). Upper Saddle River, NJ: Prentice-Hall.

    Google Scholar 

  36. Xiao, H., & Banihashemi, A. H. (2009). Error rate estimation of low-density parity-check codes on binary symmetric channels using cycle enumeration. IEEE Trans. Communications,57(6), 1550–1555.

    Google Scholar 

  37. Karimi, M., & Banihashemi, A. H. (2014). On characterization of elementary trapping sets of variable-regular LDPC codes. IEEE Transactions on Information Theory,60(9), 5188–5203.

    Google Scholar 

  38. Halford, T. R., & Chugg, K. M. (2006). An algorithm for counting short cycles in bipartite graphs. IEEE Transactions on Information Theory,52(1), 287–292.

    Google Scholar 

  39. Asvadi, R., Banihashemi, A. H., & Attari, M. A. (2011). Lowering the error floor of LDPC codes using cyclic liftings. IEEE Transactions on Information Theory,57(4), 2213–2224.

    Google Scholar 

  40. Karimi, M., & Banihashemi, A. H. (2012). Efficient algorithm for finding dominant trapping sets of LDPC codes. IEEE Transactions on Information Theory,58(11), 6942–6958.

    Google Scholar 

  41. Hashemi, Y., & Banihashemi, A. H. (2015). On characterization and efficient exhaustive search of elementary trapping sets of variable-regular LDPC codes. IEEE Communications Letters,19(3), 323–326.

    Google Scholar 

  42. Tanner, R. (1981). A recursive approach to low complexity codes. IEEE Transactions on Information Theory,27(5), 33–47.

    Google Scholar 

  43. Ryan, W. E., & Lin, S. (2009). Channel codes: Classical and modern (1st ed.). Cambridge: Cambridge University Press.

    Google Scholar 

  44. Kocarev, L., Lehmann, F., Maggio, G., Scanavino, B., et al. (2006). Nonlinear dynamics of iterative decoding systems: Analysis and applications. IEEE Transactions on Information Theory,52, 1366–1384.

    Google Scholar 

  45. Forney, G. D. (1997). On iterative decoding and the two-way algorithm. In Proceedings of international symposium on turbo codes and related topics brest, France (pp. 12–25).

  46. Matuz, B., Paolini, E., Zabini, F., & Liva, G. (2017). Non-binary LDPC code design for the Poisson PPM channel. IEEE Transactions on Communications,65(11), 4600–4611.

    Google Scholar 

  47. Vatta, F., Soranzo, A., & Babich, F. (2018). Low-complexity bound on irregular LDPC belief-propagation decoding thresholds using a Gaussian approximation. Electronics Letters,54(17), 1038–1040.

    Google Scholar 

  48. Clevorn, T., & Vary P. (2004). Low-complexity belief propagation by approximations with lookup-tables. In Proceedings of 5th international ITG conference on source and channel coding (SCC), Erlangen, Germany (pp. 211–216).

  49. Wadayama, T., Nakamura, K., Yagita, M., et al. (2010). Gradient descent bit flipping algorithms for decoding LDPC codes. IEEE Transactions on Communications,58(6), 1610–1614.

    Google Scholar 

  50. Sundararajan, G., Winstead, C., & Boutillon, E. (2014). Noisy gradient descent bit-flip decoding for decoding LDPC codes. IEEE Transactions on Communications,62(10), 3385–3400.

    Google Scholar 

  51. Huang, Q., Song, L., & Wang, Z. (2017). Set message-passing decoding algorithms for regular non-binary LDPC codes. IEEE Transactions on Communications,65(12), 5110–5122.

    Google Scholar 

  52. Davey, M. C., & MacKay, D. J. C. (1998). Low density parity check codes over GF(q). Information theory workshop.

  53. MacKay, D. J. C., Wilson, S. T., & Davey, M. C. (1999). Comparison of constructions of irregular Gallager codes. IEEE Transactions on Communications,47(10), 1449–1454.

    Google Scholar 

  54. Li, Z., Chen. L., Zeng, L., Lin, S., & Fong, F. H. (2006). Efficient encoding of quasi-cyclic low-density parity-check codes 54(1), 71–81.

  55. Huang, Q., Tang, L., He, S., Xiong, Z., & Wang, Z. (2014). Low-complexity encoding of quasi-cyclic codes based on Galois fourier transform. IEEE Transactions on Communications,62(6), 1757–1767.

    Google Scholar 

  56. Zhang, J., & Fossorier, M. P. C. (2004). A modified weighted bit-flipping decoding of low-density parity-check codes. IEEE Communications Letters,8(3), 165–167.

    Google Scholar 

  57. Nouh, A., & Banihashemi, A. H. (2002). Bootstrap decoding of low-density parity-check codes. IEEE Communications Letters,6(9), 391–393.

    Google Scholar 

  58. Oh, J., & Ha, J. (2018). A two-bit weighted bit-flipping decoding algorithm for LDPC codes. IEEE Communications Letters,22(5), 874–877.

    Google Scholar 

  59. Li, E., Gunnam, K., & Declercq, D. (2011). Trellis based extended Min-Sum for decoding non-binary LDPC codes. In Proceedings of IEEE international symposium on wireless communication systems (pp. 46–50).

  60. Davey, M. C., & MacKay, D. J. C. (1998). Low density parity check codes over GF(q). Ireland: ITW.

    Google Scholar 

  61. Sason, I., & Shamai, S. (2000). Improved upper bounds on the ensemble performance of ML decoded low density parity check codes. IEEE Communication Letters,4(3), 88–91.

    Google Scholar 

  62. Healy, C., Shao, Z., Oliveira, R. M., et al. (2018). Knowledge-aided informed dynamic scheduling for LDPC decoding of short blocks. IET Communications,12(9), 1094–1101.

    Google Scholar 

  63. Korada, S. B., Soglu, S., & Urbanke, R. (2010). Polar codes: Characterization of exponent, bounds, constructions. IEEE Transactions on Information Theory,56(12), 6253–6264.

    Google Scholar 

  64. Mughal, S., Yang, F., Xu, H., et al. (2018). Coded cooperative spatial modulation based on multi-level construction of polar code. Telecommunications Systems. https://doi.org/10.1007/s11235-018-0485-6.

    Article  Google Scholar 

  65. Fossorier, M. P. C. (2001). Iterative reliability-based decoding of low-density parity check codes. IEEE Journal on Selected Areas in Communications,19(5), 908–917.

    Google Scholar 

  66. Wu, X., Jiang, M., & Zhao, C. (2017). A parity structure for scalable QC-LDPC codes with all nodes of degree three. IEEE Communications Letters,21(9), 1913–1916.

    Google Scholar 

  67. Chen, C., Wang, L., & Liu, S. (2018). The design of protograph LDPC codes as source codes in a JSCC system. IEEE Communications Letters,22(4), 672–675.

    Google Scholar 

  68. Shahbaz, S., Akhbari, B., & Asvadi, R. (2018). LDPC codes over Gaussian multiple access wiretap channel. IET Communications,12(8), 962–969.

    Google Scholar 

  69. Kim, M., Kim, B. H., & Ahn, J. K. (2017). Secure polar coding with REP and XOR coding. IEEE Communications Letters,21(10), 2126–2129.

    Google Scholar 

  70. Shao, S., Hailes, P., Wang, T.-Y., Wu, J.-Y., Maunder, R. G., Al-Hashimi, B. M., & Hanzo, L. (2019). Survey of turbo, LDPC and polar decoder ASIC implementations. IEEE Communications Surveys & Tutorials.

  71. Chen, K., Niu, K., & Lin, J. R. (2012). List successive cancellation decoding of polar codes. IEEE Electronics Letters,48(9), 500–501.

    Google Scholar 

  72. Kong, B. Y., Yoo, H., & Park, I. C. (2016). Efficient sorting architecture for successive cancellation list decoding of polar codes. IEEE Transactions on Circuits and Systems II: Express Briefs,63(7), 673–677.

    Google Scholar 

  73. Bocharova, I. E., Kudryashov, B. D., Skachek, V., & Yakimenka, Y. (2018). BP-LED decoding algorithm for LDPC codes over AWGN channels. IEEE Transactions on Information Theory,65(3), 1677–1693.

    Google Scholar 

  74. Boutillon, E. (2018). Optimization of non binary parity check coefficients. IEEE Transactions on Information Theory,65(4), 2092–2100.

    Google Scholar 

  75. Khazraie, S., Asvadi, R., & Banihashemi, A. H. (2012). A PEG construction of finite-length LDPC codes with low error floor. IEEE Communications Letters,16(8), 1288–1291.

    Google Scholar 

  76. Hashemi, S., Balatsoukas-Stimming, & Giard, P. (2016). Partitioned successive-cancellation list decoding of polar codes. In Proceedings of IEEE international conference on acoustics, speech and signal process. Shanghai, China (pp. 957–960).

  77. Hashemi, S., Mondelli, M., & Hamed, S. (2018). Decoder partitioning: Towards practical list decoding of polar codes. IEEE Transactions on Communications,66(9), 3749–3759.

    Google Scholar 

  78. Chen, P., Bai, B., Ren, Z., Wang, J., & Sun, S. (2019). Hash-polar codes with application to 5G. IEEE Access,7, 12441–12455.

    Google Scholar 

  79. Wang, P., Yin, L., & Lu, J. (2018). Efficient helicopter-satellite communication scheme based on check-hybrid LDPC coding. Tsinghua Science and Technology,23(3), 323–332.

    Google Scholar 

  80. Yang, Y., Wang, W., & Gao, X. (2018). AMP Dual-turbo iterative detection and decoding for LDPC coded multibeam MSC uplink. China Communications,15(6), 178–186.

    Google Scholar 

  81. Azeem, M. M., Khan, A. B., & Azeem, U. (2017). Application of short erasure correcting codes for cognitive radio. In IEEE 86th vehicular technology conference (VTC-Fall).

  82. Azmi, M. H., & Leib, Harry. (2018). Multichannel cooperative spectrum sensing that integrates channel decoding with fusion-based decision. IEEE Transactions on Aerospace and Electronic Systems,54(4), 1998–2014.

    Google Scholar 

  83. Soliman, Samir S., & Song, Bongyong. (2017). Fifth generation (5G) cellular and the network for tomorrow: Cognitive and cooperative approach for energy savings. JNCA,85(1), 84–93.

    Google Scholar 

  84. Wang, X., Ge, T., Li, J., & Su, C. (2017). Efficient multi-rate encoder of QC-LDPC codes based on FPGA for WIMAX Standard. Chinese Journal of Electronics,26(2), 250–255.

    Google Scholar 

  85. Uthansakul, M., & Uthansakul, P. (2011). Experiments with a low-profile beamforming MIMO system for WLAN applications. IEEE Antennas and Propagation Magazine,53(6), 56–69.

    Google Scholar 

  86. Tsatsaragkos, I., & Paliouras, V. (2018). A reconfigurable LDPC decoder optimized for 802.11n/ac applications. IEEE Transactions on Very Large Scale Integration,26(1), 182–195.

    Google Scholar 

  87. Pellenz, M. E., Souza, D. R., & Fonseca, M. S. P. (2010). Error control coding in wireless sensor networks. Telecommunication Systems,44(1), 61–68.

    Google Scholar 

  88. Tsai, H.-C. (2019). Iterative multiuser detector-decoding for nonbinary LDPC coded multicarrier MFSK systems. Telecommunication Systems,70(2), 309–320.

    Google Scholar 

  89. Hamming, R. W. (1950). Error detecting and error correcting codes. Bell System Technical Journal,29(2), 147–160.

    Google Scholar 

  90. Golay, M. J. (1949). Notes on digital coding. In Proceedings of the IRE (vol. 37, p. 657).

  91. Muller, D. E. (1954). Application of boolean algebra to switching circuit design and to error detection. Electronic Computers, Transactions of the IRE Professional Group,3, 6–12.

    Google Scholar 

  92. Reed, I. (1954). A class of multiple-error-correcting codes and the decoding scheme. Information Theory, Transactions of the IRE Professional Group,4(4), 38–49.

    Google Scholar 

  93. Bose, R. C., & Ray-Chaudhuri, D. K. (1960). On a class of error correcting binary group codes. Information and Control,3(1), 68–79.

    Google Scholar 

  94. Reed, I. S., & Solomon, G. (1960). Polynomial codes over certain finite fields. Journal of the Society for Industrial and Applied Mathematics,8(2), 300–304.

    Google Scholar 

  95. Costello, D. J., & Forney, G. D. (2007). Channel coding: The road to channel capacity. Proceedings of the IEEE,95, 1150–1177.

    Google Scholar 

  96. Elias P. (1955). Coding for two noisy channels. In Proceedings Th. Theory (pp. 61–76).

  97. Viterbi, A. J. (1967). Error bounds for convolutional codes and an asymptotically optimum decoding algorithm. IEEE Transactions on Information Theory,13(2), 260–269.

    Google Scholar 

  98. Bahl, L., Cocke, J., Jelinek, F., & Raviv, J. (1974). Optimal decoding of linear codes for minimizing symbol error rate. IEEE Transactions on Information Theory,20(2), 284–287.

    Google Scholar 

  99. Consulative Committee for Space Data Systems (CCSDS). (1984).Telemetry channel coding. Silver Book.

  100. Gallager, R. G. (1963). Low-density parity-check codes. Ph.D. thesis, Dep. Electrical Eng., M.I.T, Cambridge.

  101. Arıkan, E. (2008). A performance comparison of polar codes and Reed–Muller Codes. IEEE Communications Letters,12(6), 447–449.

    Google Scholar 

  102. Liang, H., Liu, A., Zhang, Y., & Zhang, Q. (2017). Analysis and adaptive design of polar coded HARQ transmission under SC-list decoding. IEEE Wireless Communications Letters,6(6), 798–801.

    Google Scholar 

  103. Niu, K., & Chen, K. (2012). Stack decoding of polar codes. Electronics Letters,48(12), 695–696.

    Google Scholar 

  104. Chen, K., Niu, K., & Lin, Jiaru. (2013). Improved successive cancellation decoding of polar codes. IEEE Transactions on Communications,61(8), 3100–3107.

    Google Scholar 

  105. Li, B., Shen, H., & Tse, D. (2012). An adaptive successive cancellation list decoder for polar codes with cyclic redundancy check. IEEE Communications Letters,16(12), 2044–2047.

    Google Scholar 

  106. Niu, K., & Chen, K. (2012). CRC-aided decoding of polar codes. IEEE Communications Letters,16(10), 1668–1671.

    Google Scholar 

  107. Elkelesh, A., Ebada, M., Cammerer, S., & ten Brin, Stephan. (2018). Belief propagation list decoding of polar codes. IEEE Communication Letters,22(8), 1536–1539.

    Google Scholar 

  108. OnurDizdar, Erdal Arıkan. (2016). A high-throughput energy-efficient implementation of successive cancellation decoder for polar codes using combinational logic. IEEE Transactions on Circuits and Systems,63(3), 436–447.

    Google Scholar 

  109. Jiang, S., Mo, F., Lau, C. M., & Sham, C. W. (2018). Tree-permutation-matrix based LDPC codes. IEEE Transactions on Circuits and Systems,65(8), 1019–1023.

    Google Scholar 

  110. Kim, K. S., Lee, S. H., Kim, Y. H., & Ahn, J. Y. (2004). Design of binary LDPC code using cyclic shift matrices. Electronics letters,40(5), 325–326.

    Google Scholar 

  111. Tasdighi, A., Banihashemi, A. H., & Sadeghi, M. R. (2017). Symmetrical constructions for regular Girth-8 QC-LDPC codes. IEEE Transactions on Communications,65(1), 14–22.

    Google Scholar 

  112. Diao, Q., Li, J., Lin, S., & Blake, I. F. (2016). New classes of partial geometries and their associated LDPC codes. IEEE Transactions on Information Theory,62(6), 2947–2965.

    Google Scholar 

  113. Elsanadily, S., Mahran, A., & Elghandour, O. (2018). Classification-based algorithm for bit-flipping decoding of GLDPC codes over AWGN channels. IEEE Communications Letters,22(8), 1520–1523.

    Google Scholar 

  114. He, X., Zhou, L., & Du, J. (2018). PEG-like design of binary QC-LDPC codes based on detecting and avoiding generating small cycles. IEEE Transactions on Communications,66(5), 1845–1858.

    Google Scholar 

  115. Jiang, X. Q., Hai, H., Wang, H. M., & Lee, M. H. (2017). Constructing large Girth QC protograph LDPC codes based on PSD-PEG algorithm. IEEE Access,5, 13489–13500.

    Google Scholar 

  116. Jiang, X., Xia, X. G., & Lee, M. H. (2014). Efficient progressive edge-growth algorithm based on Chinese remainder theorem. IEEE Transactions on Communications,62(2), 442–451.

    Google Scholar 

  117. Gruner, A., & Huber, M. (2012). New combinatorial construction techniques for low-density parity-check codes and systematic repeat-accumulate codes. IEEE Transactions on Communications,60(9), 2387–2395.

    Google Scholar 

  118. Wei, X., & Akansu, A. (2001). Density evolution for low-density parity-check codes under Max-Log-MAP decoding. Electronics Letters,37(18), 1125–1126.

    Google Scholar 

  119. Mao, Y., & Banihashemi, A. H. (2001). Decoding low-density parity-check codes with probabilistic scheduling. IEEE Commuincation on Letters,5(10), 414–416.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Komal Arora.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Arora, K., Singh, J. & Randhawa, Y.S. A survey on channel coding techniques for 5G wireless networks. Telecommun Syst 73, 637–663 (2020). https://doi.org/10.1007/s11235-019-00630-3

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11235-019-00630-3

Keywords

Navigation