Symbol-Based Belief Propagation Decoder for Multilevel Polar Coded Modulation

In this letter, symbol-based belief propagation decoder is proposed for multilevel polar coded modulation (MLPCM) scheme. Unlike the traditional multi-stage detection (MSD) strategy by decoding polar codes level by level after demapping, we directly calculate the probabilities of symbols and do demapping after the symbol decoding process so as to decrease the decoding delay and improve the performance of MLPCM. The lower bound of frame error rate for MLPCM is also estimated using the union bound technique. Numerical results show that the performance of proposed decoder well matches the estimated bound for pulse amplitude modulation (PAM) modulation and outperforms the MSD strategy about 0.5−1 dB with lower decoding delay, only at the cost of some additional computational complexity, which indicates its effectiveness.

[1]  Andreas Schenk,et al.  Polar-Coded Modulation , 2013, IEEE Transactions on Communications.

[2]  Andreas Schenk,et al.  Aspects of Polar-Coded Modulation , 2012, ArXiv.

[3]  Yuping Zhao,et al.  Optimum asymmetric constellation design for trellis-coded modulation over gaussian channels , 2009, IEEE Communications Letters.

[4]  Jungwon Lee,et al.  Polar Coding for Bit-Interleaved Coded Modulation , 2016, IEEE Transactions on Vehicular Technology.

[5]  Srinath Hosur,et al.  On the design of binary polar codes for high-order modulation , 2014, 2014 IEEE Global Communications Conference.

[6]  John R. Barry,et al.  Low-Complexity Soft-Output Decoding of Polar Codes , 2014, IEEE Journal on Selected Areas in Communications.

[7]  Kai Chen,et al.  Polar Coded Modulation with Optimal Constellation Labeling , 2013, ArXiv.

[8]  Mehrdad Valipour,et al.  On Probabilistic Weight Distribution of Polar Codes , 2013, IEEE Communications Letters.

[9]  Aijun Liu,et al.  Practical Design and Decoding of Parallel Concatenated Structure for Systematic Polar Codes , 2016, IEEE Transactions on Communications.

[10]  E. Kurtas,et al.  Performance bounds for high rate linear codes over partial response channels , 2000, 2000 IEEE International Symposium on Information Theory (Cat. No.00CH37060).

[11]  Robert F. H. Fischer,et al.  Multilevel codes: Theoretical concepts and practical design rules , 1999, IEEE Trans. Inf. Theory.

[12]  Alexander Vardy,et al.  List decoding of polar codes , 2011, 2011 IEEE International Symposium on Information Theory Proceedings.

[13]  Emanuele Viterbo,et al.  Multiple Folding for Successive Cancelation Decoding of Polar Codes , 2014, IEEE Wireless Communications Letters.

[14]  Erdal Arikan.  Channel combining and splitting for cutoff rate improvement , 2006, IEEE Transactions on Information Theory.

[15]  Erdal Arikan,et al.  Channel Polarization: A Method for Constructing Capacity-Achieving Codes for Symmetric Binary-Input Memoryless Channels , 2008, IEEE Transactions on Information Theory.