Abstract
This paper proposes a mapping design for bit-interleaved polar coded modulation (BIPCM) systems with belief propagation (BP) decoding. We first introduce a two-layer bipartite graph to represent BIPCM, where a new mapping graph linking polar graph to modulator is added to the conventional factor graph. Then, a mapping design is proposed and the design paradigm is to separate sub-channels with lower reliability to different stopping trees of polar codes, aiming to make sure that each stopping tree receives reliable extrinsic information from demodulator. The proposed mapping algorithm is employed for BIPCM with traditional polar codes over 16-quadrature amplitude modulation (QAM) and 256-QAM. Numerical results show that our scheme can improve the error-correcting performance compared to the conventional scheme with a random mapping. Furthermore, to meet code-length requirement of different modulation orders, we propose an efficient method to construct flexible-length polar code (FLPC) by coupling several short length polar codes with a repeat-accumulate (RA) code. Also, the proposed FLPC is employed in the BIPCM system, with the designed mapping algorithm, simulation result also reveals that the block error rate performance of proposed BIPCM scheme with BP decoding outperforms the one with successive cancellation decoding by providing a gain up to 1 dB.
Highlights
Polar codes, invented by Arıkan in 2009 [1], have been proven to achieve the symmetric capacity of binary-input discrete memoryless channels (BDMCs) with successive cancellation (SC) decoding
3) To meet the code-length requirements brought by different modulation orders, we introduce a method to construct flexible-length polar code (FLPC), by coupling several short length polar codes with a repeat-accumulate (RA) code
Besides belief propagation (BP) decoding, soft cancellation (SCAN) decoding is considered for polar codes in FLPC and the maximum iteration is Imax = 15
Summary
Polar codes, invented by Arıkan in 2009 [1], have been proven to achieve the symmetric capacity of binary-input discrete memoryless channels (BDMCs) with successive cancellation (SC) decoding. This property for polar codes over the factor graph has been well utilized to improve the performance of iterative decoding [17]–[21] Motivated by these observations, in this paper we consider the mapping design for the BIPCM scheme with BP decoding taking both the properties of polar codes over the factor graph and the unequal error protection property of high-order modulations into account. Simulation results demonstrate that a combination of the proposed FLPC and the designed mapping with BP decoding provides a frame error rate FER) performance gain of about 1 dB over the one of the compound polar coded BICM scheme with SC decoding [6], when 64-QAM is implemented over the AWGN channel.
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