, Generation Partnership Project (3GPP), 2018.

A. Abdmouleh, A new approach to optimise Non-Binary LDPC codes for Coded Modulations, 9th International Symposium on Turbo Codes and Iterative Information Processing, pp.295-299, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01365554

A. Orion-a-siadis, A. Balatsoukas-stimming, and . Burg, A low-complexity improved successive cancellation decoder for polar codes, 48th Asilomar Conference on Signals, Systems and Computers, pp.2116-2120, 2014.

A. Alamdar, -. Yazdi, and . Frank-r-kschischang, A simpli ed successive-cancellation decoder for polar codes, IEEE communications letters 15, vol.12, pp.1378-1380, 2011.

E. Arikan, Channel polarization: A method for constructing capacity-achieving codes for symmetric binary-input memoryless channels, IEEE Transactions on Information Theory, vol.55, pp.3051-3073, 2009.

E. Arikan, Performance of short polar codes under ML decoding, ICT-Mobile Summit Conf. Proc, 2009.

V. Bakoev, One more way for counting monotone boolean functions, Thirteenth International Workshop on Algebraic and Combinatorial Coding Theory, p.4752, 2012.

A. Balatsoukas-stimming, M. Bastani-parizi, and A. Burg, LLR-based successive cancellation list decoding of polar codes, IEEE transactions on signal processing, vol.63, pp.5165-5179, 2015.

M. Bardet, Algebraic properties of polar codes from a new polynomial formalism, IEEE International Symposium on Information Theory (ISIT), pp.230-234, 2016.
URL : https://hal.archives-ouvertes.fr/hal-01410210

M. Bastani and P. , Polar Codes: Finite Length Implementation, Error Correlations and Multilevel Modulation, 2012.

M. Benammar, Multi-kernel polar codes: Proof of polarization and error exponents, Information Theory Workshop, pp.101-105, 2017.

G. Berhault, Exploration architecturale pour le décodage de codes polaires, 2015.

R. Elwyn, N. Berlekamp, and . Sloane, Restrictions on weight distribution of Reed-Muller codes, Information and Control, vol.14, pp.442-456, 1969.

V. Bioglio, C. Condo, and I. Land, Design of Polar Codes in 5G New Radio, 2018.

V. Bioglio, F. Gabry, and I. Land, Low-Complexity Puncturing and Shortening of Polar Codes, IEEE Wireless Communications and Networking Conference Workshops, pp.1-6, 2017.

V. Bioglio, Minimum-Distance Based Construction of Multi-Kernel Polar Codes, 2017.

S. Buzaglo, On E cient Decoding of Polar Codes with Large Kernels, IEEE Wireless Communications and Networking Conference Workshops, pp.1-6, 2017.

G. Caire, G. Taricco, and E. Biglieri, Bit-interleaved coded modulation, IEEE Transactions on Information Theory, vol.44, pp.927-946, 1998.

L. Chandesris, V. Savin, and D. Declercq, An Improved SCFlip for Polar Codes, IEEE Global Communications Conference (GLOBECOM), pp.1-6, 2016.
URL : https://hal.archives-ouvertes.fr/cea-01573437

L. Chandesris, V. Savin, and D. Declercq, Dynamic-SCFlip decoding of polar codes, IEEE Transactions on Communications, 2018.
URL : https://hal.archives-ouvertes.fr/hal-01742725

K. Chen, K. Niu, and J. Lin, An e cient design of bit-interleaved polar coded modulation, IEEE 24th International Symposium on Personal Indoor and Mobile Radio Communications (PIMRC), pp.693-697, 2013.

K. Chen, K. Niu, and J. Lin, Practical polar code construction over parallel channels, IET Communications, vol.7, pp.620-627, 2013.

K. Chen, K. Niu, and J. Lin, Improved successive cancellation decoding of polar codes, IEEE Transactions on Communications, vol.61, pp.3100-3107, 2013.

P. Chen, B. Bai, and X. Ma, A New Construction of Nonbinary Polar Codes with Two-stage Polarization, 2018.

S. Chung, On the design of low-density parity-check codes within 0.0045 dB of the Shannon limit, IEEE Communications letters, vol.5, pp.58-60, 2001.

G. Coppolino, A Multi-Kernel Multi-Code Polar Decoder Architecture, 2018.

J. Dai, Does gaussian approximation work well for the long-length polar code construction?, In: IEEE Access, vol.5, pp.7950-7963, 2017.

D. Declercq and M. Fossorier, Decoding algorithms for nonbinary LDPC codes over GF (q), IEEE Transactions on Communications, vol.55, pp.633-643, 2007.

P. Elias, Coding for two noisy channels, IRE International Convention Record, pp.37-46, 1955.

A. Elkelesh, Belief propagation decoding of polar codes on permuted factor graphs, Wireless Communications and Networking Conference (WCNC), pp.1-6, 2018.

F. Ercan, C. Condo, and W. Gross, Improved Bit-Flipping Algorithm for Successive Cancellation Decoding of Polar Codes, 2018.

F. Ercan, Partitioned Successive-Cancellation Flip Decoding of Polar Codes, International Conference on Communications (ICC), pp.1-6, 2018.

U. Ubaid, J. Fayyaz, and . Barry, Low-complexity soft-output decoding of polar codes, IEEE Journal on Selected Areas in Communications, vol.32, pp.958-966, 2014.

A. Fazeli and A. Vardy, On the scaling exponent of binary polarization kernels, 52nd Annual Allerton Conference on Communication, Control, and Computing, pp.797-804, 2014.

D. Forney, Codes on graphs: normal realizations, IEEE Transactions on Information Theory, vol.47, pp.520-548, 2001.

. Gallagher, Low-density parity-check codes, no. 21 in Research Monograph Series, 1963.

P. Giard and A. Burg, Fast-SSC-ip decoding of polar codes, Wireless Communications and Networking Conference Workshops, pp.73-77, 2018.

P. Giard, C. Thibeault, and W. Gross, High-speed decoders for polar codes, 2017.

M. Talha-cihad-gulcu, A. Ye, and . Barg, Construction of polar codes for arbitrary discrete memoryless channels, IEEE Transactions on Information Theory, vol.64, pp.309-321, 2018.

J. Guo and A. Guillen-i-fabregas, E cient sphere decoding of polar codes, IEEE International Symposium on Information Theory (ISIT, pp.236-240, 2015.

A. Seyyed, C. Hashemi, W. Condo, and . Gross, Simpli ed successive-cancellation list decoding of polar codes, IEEE International Symposium on Information Theory (ISIT), pp.815-819, 2016.

K. Seyed-hamed-hassani, R. Alishahi, and . Urbanke, Finite-length scaling for polar codes, IEEE Transactions on Information Theory, vol.60, pp.5875-5898, 2014.

G. He, ?-expansion: A Theoretical Framework for Fast and Recursive Construction of Polar Codes, 2017.

Z. Huang, On the Successive Cancellation Decoding of Polar Codes with Arbitrary Linear Binary Kernels, p.0, 2017.

J. Huber and U. Wachsmann, Capacities of equivalent channels in multilevel coding schemes, Electronics Letters, vol.30, pp.557-558, 1994.

N. Hussami, R. Satish-babu-korada, and . Urbanke, Performance of polar codes for channel and source coding, IEEE International Symposium on Information Theory, pp.1488-1492, 2009.

H. Imai and S. Hirakawa, A new multilevel coding method using error-correcting codes, IEEE Transactions on Information Theory, vol.23, pp.371-377, 1977.

. Corina-i-ionita, On the design of binary polar codes for high-order modulation, IEEE Global Communications Conference (GLOBECOM), pp.3507-3512, 2014.

O. ??can, R. Böhnke, and W. Xu, Shaped Polar Codes for Higher Order Modulation, IEEE Communications Letters, vol.22, pp.252-255, 2018.

O. ??can and W. Xu, Polar Codes with Integrated Probabilistic Shaping for 5G New Radio, 2018.

R. Johannesson and K. Sh-zigangirov, Fundamentals of convolutional coding, vol.15, 2015.

S. Kahraman and . Mehmet-ertugrul-celebi, Code based e cient maximum-likelihood decoding of short polar codes, IEEE International Symposium on Information Theory (ISIT), pp.1967-1971, 2012.

D. Kern, S. Vorkoper, and V. Kuhn, A new code construction for polar codes using min-sum density, 8th International Symposium on Turbo Codes and Iterative Information Processing, pp.228-232, 2014.

J. Kim, J. Kim, and S. Kim, An e cient search on puncturing patterns for short polar codes, International Conference on Information and Comm. Tech. Convergence (ICTC, pp.182-184, 2015.

E. Satish-babu-korada, R. Sasoglu, and . Urbanke, Polar codes: Characterization of exponent, bounds, and constructions, IEEE Transactions on Information Theory, vol.56, pp.6253-6264, 2010.

J. Rey and C. Lagarias, The Takagi function and its properties, 2011.

S. L. Go, A. Glavieux, and C. Berrou, Turbo-codes and high spectral e ciency modulation, IEEE International Conference on Communications. INSTITUTE OF ELECTRICAL ENGINEERS INC, pp.645-645, 1994.

M. Lee and K. Yang, The exponent of a polarizing matrix constructed from the Kronecker product, Designs, codes and cryptography, vol.70, pp.313-322, 2014.

C. Leroux, Hardware architectures for successive cancellation decoding of polar codes, International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp.1665-1668, 2011.
URL : https://hal.archives-ouvertes.fr/hal-00670695

H. Lin, S. Lin, and K. Ar, Binary nonlinear kernels of maximum exponents of polar codes of dimensions up to sixteen, IEEE International Symposium on Information Theory (ISIT, pp.221-225, 2015.

J. C. David, . Mackay, M. Radford, and . Neal, Near Shannon limit performance of low density parity check codes, Electronics letters, vol.32, pp.1645-1646, 1996.

V. Miloslavskaya, Shortened polar codes, IEEE Transactions on Information Theory, vol.61, pp.4852-4865, 2015.

V. Miloslavskaya and P. Trifonov, Sequential decoding of polar codes, IEEE Communications Letters, vol.18, pp.1127-1130, 2014.

M. Mondelli, R. Hamed-hassani, and . Urbanke, Construction of Polar Codes with Sublinear Complexity, 2016.

M. Mondelli, R. L. Hamed-hassani, and . Urbanke, From polar to Reed-Muller codes: a technique to improve the nite-length performance, IEEE Transactions on Communications, vol.62, pp.3084-3091, 2014.

M. Mondelli, R. Hamed-hassani, and . Urbanke, Scaling exponent of list decoders with applications to polar codes, IEEE Transactions on Information Theory, vol.61, pp.4838-4851, 2015.

M. Mondelli, R. Hamed-hassani, and . Urbanke, Uni ed scaling of polar codes: Error exponent, scaling exponent, moderate deviations, and error oors, IEEE Transactions on Information Theory, vol.62, pp.6698-6712, 2016.

R. Mori and T. Tanaka, Channel polarization on q-ary discrete memoryless channels by arbitrary kernels, International Symposium on Information Theory Proceedings (ISIT). IEEE. 2010, pp.894-898

R. Mori and T. Tanaka, Non-binary polar codes using Reed-Solomon codes and algebraic geometry codes, Information Theory Workshop (ITW). IEEE. 2010, pp.1-5

R. Mori and T. Tanaka, Performance and construction of polar codes on symmetric binary-input memoryless channels, IEEE International Symposium on Information Theory, pp.1496-1500, 2009.

E. David and . Muller, Application of Boolean algebra to switching circuit design and to error detection, Transactions of the IRE Professional Group on Electronic Computers, vol.3, pp.6-12, 1954.

K. Niu and . Chen, Stack decoding of polar codes, Electronics letters, vol.48, pp.695-697, 2012.

K. Niu, K. Chen, and J. Lin, Beyond turbo codes: rate-compatible punctured polar codes, International Conference on Communications (ICC), pp.3423-3427, 2013.

K. Niu, Rate-Compatible Punctured Polar Codes: Optimal Construction Based on Polar Spectra, 2016.

C. Poulliat, M. Fossorier, and D. Declercq, Design of regular (2, d/sub c/)-LDPC codes over GF (q) using their binary images, IEEE Transactions on Communications, vol.56, 2008.

N. Presman, O. Shapira, and S. Litsyn, Mixed-Kernels Constructions of Polar Codes, IEEE Journal on Selected Areas in Communications, vol.34, pp.239-253, 2015.

T. Prinz, Polar coded probabilistic amplitude shaping for short packets, 18th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC). IEEE. 2017, pp.1-5

M. Qin, Polar Code Constructions Based on LLR Evolution, 2017.

S. Irving, G. Reed, and . Solomon, Polynomial codes over certain nite elds, Journal of the society for industrial and applied mathematics, vol.8, pp.300-304, 1960.

J. Thomas, . Richardson, and . Rüdiger-l-urbanke, The capacity of low-density parity-check codes under message-passing decoding, IEEE Transactions on Information Theory, vol.47, pp.599-618, 2001.

S. Roman, Coding and information theory, vol.134, 1992.

H. Saber and I. Marsland, An incremental redundancy hybrid ARQ scheme via puncturing and extending of polar codes, IEEE Transactions on Communications, vol.63, pp.3964-3973, 2015.

G. Sarkis, Fast list decoders for polar codes, IEEE Journal on Selected Areas in Communications, vol.34, pp.318-328, 2016.

G. Sarkis, Fast polar decoders: Algorithm and implementation, IEEE Journal on Selected Areas in Communications, vol.32, pp.946-957, 2014.

E. ?a?o?lu, E. Telatar, and E. Arikan, Polarization for arbitrary discrete memoryless channels, Information Theory Workshop, pp.144-148, 2009.

P. Schláfer, A new architecture for high throughput, low latency NB-LDPC check node processing, 26th Annual International Symposium on Personal, pp.1392-1397, 2015.

C. Schürch, A partial order for the synthesized channels of a polar code, IEEE International Symposium on Information Theory (ISIT), pp.220-224, 2016.

. Bibliographie,

M. Seidl, Aspects of polar-coded modulation, 9th International ITG Conference on Systems, Communication and Coding (SCC), Proceedings o. VDE. 2013, pp.1-6

M. Seidl, Polar-coded modulation, IEEE Transactions on Communications, vol.61, pp.4108-4119, 2013.

E. Claude, W. Shannon, and . Weaver, The Mathematical Theory of Information, 1949.

D. Shin, S. Lim, and K. Yang, Design of length-compatible polar codes based on the reduction of polarizing matrices, IEEE Transactions on Communications, vol.61, pp.2593-2599, 2013.

D. Shin, S. Lim, and K. Yang, Mapping selection and code construction for 2?m-ary polar-coded modulation, IEEE Communications Letters, vol.16, issue.6, pp.905-908, 2012.

N. Stolte, Recursive codes with the Plotkin-Construction and their Decoding

I. Tal and A. Vardy, How to construct polar codes, IEEE Transactions on Information Theory, vol.59, pp.6562-6582, 2013.

I. Tal and A. Vardy, List decoding of polar codes, IEEE International Symposium on Information Theory (ISIT), pp.1-5, 2011.

I. Tal and A. Vardy, List decoding of polar codes, IEEE Transactions on Information Theory, vol.61, pp.2213-2226, 2015.

. Saurabha-r-tavildar, Bit-permuted coded modulation for polar codes, IEEE Wireless Communications and Networking Conference Workshops, pp.1-6, 2017.

P. Trifonov, E cient design and decoding of polar codes, IEEE Transactions on Communications, vol.60, issue.11, pp.3221-3227, 2012.

P. Trifonov, Reduced complexity decoding of polar codes with Reed-Solomon kernel

P. Trifonov, V. Miloslavskaya, and R. Morozov, Fast Sequential Decoding of Polar Codes, 2017.

G. Tro and P. Trifonov, Block sequential decoding of polar codes, International Symposium on Wireless Communication Systems (ISWCS), pp.326-330, 2015.

G. Ungerboeck, Channel coding with multilevel/phase signals, IEEE Transactions on Information Theory, vol.28, pp.55-67, 1982.

U. Wachsmann, F. H. Robert, J. Fischer, and . Huber, Multilevel codes: Theoretical concepts and practical design rules, IEEE Transactions on Information Theory, vol.45, pp.1361-1391, 1999.

R. Wang and R. Liu, A novel puncturing scheme for polar codes, IEEE Communications Letters, vol.18, pp.2081-2084, 2014.

T. Wang, D. Qu, and T. Jiang, Parity-check-concatenated polar codes, IEEE Communications Letters, vol.20, pp.2342-2345, 2016.

N. Wiberg, H. Loeliger, and R. Kotter, Codes and iterative decoding on general graphs, European Transactions on telecommunications, vol.6, pp.513-525, 1995.

M. Wozencraft and B. Rei-en, , 1961.

. Bibliographie,

P. Yuan and F. Steiner, E cient Decoding Algorithms for Polar Codes based on 2\times2

?. Non and . Binarykernels, , 2018.

L. Zhang, On the puncturing patterns for punctured polar codes, International Symposium on Information Theory, pp.121-125, 2014.

Y. Zhang, A Practical Construction Method for Polar Codes, IEEE Communication Letter, vol.18, p.11, 2014.

Z. Zhang, Progressive Bit-Flipping Decoding of Polar Codes Over Layered Critical Sets, Global Communications Conference (Globecom, pp.1-6, 2017.