Bit-interleaved Polar Coded Modulation Research Articles

Jointly polar-coded probabilistic shaping scheme based on many-to-one mapping in IM/DD optical DMT interconnection.

A joint channel coding and probabilistic shaping (PS) scheme is proposed and experimentally demonstrated in an intensity modulation and direct-detection optical discrete multi-tone (DMT) interconnection. The PS-32 quadrature amplitude modulation (PS-32QAM) is probabilistically reshaped from a 6-bit/symbol 64QAM signal based on polar-coded many-to-one (MTO) mapping, enabling a Gaussian-like symbol probability distribution without shaping or forward error correction redundancy. A bit-interleaved polar-coded modulation iterative decoding system based on joint QAM demapping and polar decoding is employed to retrieve the multi-labeled PS symbols. Experimental results indicate that the polar-coded PS-32QAM DMT signal achieves a 1.5-dB receiver power sensitivity improvement and a 2.71-dB fiber nonlinearity tolerance enhancement over 10-km standard single-mode fiber transmission.

Performance of Adaptive Bit-Interleaved Polar Coded Modulation in FSOC System

This paper proposes an adaptive bit-interleaved polar coded modulation (A-BIPCM) method based on minimum logarithmic upper bound weight (MLUW). It is designed to reduce the fading effects and long string of bit error interference caused by atmospheric turbulence in free-space optical communications (FSOC). To assess the effectiveness of this method across turbulent channels of varying intensities, we conducted an evaluation of the bit error rate (BER) performance of polar codes in turbulent channels. The results demonstrate significant performance improvements provided by the A-BIPCM method compared to conventional polar code encoding and decoding. Specifically, under weak, moderate, and strong turbulence conditions, the A-BIPCM method achieves performance gains of 0.96 dB, 1.66 dB, and 1.35 dB, respectively. Additionally, an experimental verification platform for FSOC employing intensity modulation direct detection (IM/DD) with an atmospheric turbulence simulation channel, is established in this work. When the optical power of the detector is −16 dBm, the traditional polar code encoding and decoding performance at BER = 2.36 × 10−5, whereas the A-BIPCM scheme exhibits a significantly higher performance at BER = 2.11 × 10−6. The BER has been improved by representing an order of magnitude.

Block Polarization HARQ for Polar-Coded Modulation

In this paper, we propose a block polarization (BP) scheme as a framework to study polar-coded hybrid automatic repeat request (Polar-HARQ) under bit-interleaved polar-coded modulation (BIPCM). The BP scheme of BIPCM can combine multiple independent polar subcodes to form a longer polar code under the block polarization between polar subcodes. The BP scheme of HARQ further carries out block polarization based on the BP scheme of BIPCM, which can combine multiple transmitted BP schemes of BIPCM together to form a longer polar code. When the underlying channels are non-uniform, such as the polarization effect of high-order modulation will lead to non-uniform reliabilities, it is not suitable to use the fixed sequence (e.g., the polarization weight (PW) sequence or Polar sequence in the 5G standard) to construct polar codes. The underlying channels on each polar subcode have uniform reliability by dividing different blocks according to the reliabilities of the underlying channel. Based on this characteristic of BP scheme, we propose a rate-allocation (RA) method to study fast code construction of BP scheme. The key idea of the proposed RA method is finding out the equivalent channel whose average symmetric capacity equals the target transmission rate. The allocated rates are computed according to the symmetric capacities of split channels under the block polarization between polar subcodes. Then the ranking of bit indices within each polar subcode can be obtained by fixed sequence. In this way, the RA code construction is concise and robust for diverse configurations which are the desired features for practical implementation. Simulation results show that the proposed BP scheme under RA construction can achieve almost identical performance as the Gaussian approximation construction with much lower complexity.

Analysis and Design of Polar-Coded Modulation

Conventional design methods of polar-coded modulation schemes aim to minimize the block error rate (BLER) under successive cancellation (SC) decoding. However, codes designed by conventional methods are not competitive under successive cancellation list (SCL) decoding. This paper presents a new design method based on the BLER upper bound under maximum-likelihood (ML) decoding (ML-BLER upper bound). The ML-BLER upper bound depends on the weight enumerating function (WEF) of the polar-coded modulation scheme over the squared Euclidean distance. In this paper, the polar-coded modulation is randomized by the concept of interleaved polar (i-polar) codes, and the WEF averaged over the ensemble of the polar-coded modulation schemes can be derived. Three polar-coded modulation schemes are considered, i.e., the bit-interleaved polar-coded modulation with a single interleaver (BIPCM-SI), the bit-interleaved polar-coded modulation with multiple interleavers (BIPCM-MI), and the multi-level polar-coded modulation (MLPCM). A new bit channel selection algorithm for polar-coded modulation schemes is proposed, which takes the polarization effect and the ML-BLER upper bound as design criteria. Design examples show that, under SCL decoding, the polar-coded modulation schemes (without CRC) with the proposed channel selection algorithm outperform those with conventional algorithms and are competitive as compared to the state-of-the-art 5G LDPC codes.

Partially Information Coupled Bit-Interleaved Polar Coded Modulation

In this paper, we propose partially information coupled bit-interleaved polar coded modulation (PIC-BIPCM), which is a class of spatially coupled polar coding schemes designed for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2^{Q}$ </tex-math></inline-formula> -ary modulations. Specifically, we consider PIC-BIPCM schemes respectively constructed with three BIPCM schemes: direct BIPCM, punctured BIPCM, and multi-kernel BIPCM. We analyze the error performance of the proposed PIC-BIPCM over the binary erasure channel (BEC) via density evolution. With the analysis as a guideline, we jointly design the positions of coupled bits and the modulation bit-mapper by taking into account the partial polarization of finite length polar codes as well as the unequal error protection of high order modulations. Simulation results demonstrate significant performance improvement of the proposed PIC-BIPCM over the uncoupled BIPCM on both BEC and AWGN channels.

Performance Enhanced 256-QAM BIPCM-DMT System Enabled by CAZAC Precoding

In the paper, bit-interleaved polar-coded modulation discrete multi-tone (DMT) (BIPCM-DMT) with 256-QAM enabled by constant amplitude zero auto-correlation (CAZAC) precoding is proposed and experimentally demonstrated in a low-cost intensity-modulation and direct-detection (IM-DD) system. In order to conquer the fading effect on mapped bit-levels, two types of interleaver including quadratic polynomial permutation (QPP) interleaver and random interleaver are compared to optimize the system performance. However, for 256-QAM BIPCM-DMT system, the signal-to-noise ratio (SNR) fades dramatically as the data subcarrier index increases, it is difficult to match the well-designed operating point of Monte Carlo in the process of polar code construction. Thus, the precoding schemes including CAZAC and orthogonal circulant transform (OCT) are proposed to equalize the uneven SNRs in BIPCM-DMT system. Compared with the bit / power loading and pre-equalization schemes, it will greatly reduce the cost and complexity of the system because channel information obtained by the transmitter via round-trip feedback is not considered. In addition, CAZAC precoding is selected to optimize the BIPCM-DMT system because it is superior to OCT precoding in reducing PAPR. The experimental results show that aided by CAZAC precoding, 20.63 Gb/s BIPCM-DMT signal can be received with an error-free over 50-km standard single-mode fiber (SSMF). Furthermore, compared with BIPCM-free, only CAZAC precoding, and only random interleaver schemes, the proposed scheme can achieve Q-factor enhancement of 4.82 dB, 2.46 and 1.78 dB, respectively, at the received optical power (ROP) of −5 dBm.

Mapping Design for $2^{M}$ -Ary Bit-Interleaved Polar Coded Modulation

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.

Symbol Mapping Design for Bit-Interleaved Polar-Coded Modulation With Iterative Decoding

In this letter, we design a bit-interleaved polar-coded modulation system with iterative decoding subject to constraints on complexity, error floor, and waterfall region performance. We show that the hill-like trajectory of polar code extrinsic information transfer curves allows us to predict the gap of the bottleneck region that a polar code achieves at a given received signal-to-noise ratio for a given labeling rule. Using the gap, we propose a 3-D linear objective function to optimize for error floor, waterfall region performance, and complexity. The objective function requires Monte Carlo simulations for only three points on the extrinsic information transfer curve of the demapper for a given labeling rule. Our simulations show that the proposed method designs labeling rule and polar code duos that trade off error-floor and waterfall region performance with complexity and latency.

Bit-interleaved polar coded modulation scheme for high-order QAM encoded DDO-OFDM systems

Abstract In the paper, a simple generation scheme of the twin-SSB-OFDM signal based on one OFDM transmitter is proposed in the direct-detection optical orthogonal frequency-division multiplexing (DDO-OFDM) system. Compared with traditional generation scheme that requires two OFDM transmitters, it has lower implementation complexity and lower cost. In addition, to enhance the spectral efficiency (SE) for DDO-OFDM system, an efficient bit-interleaved polar coded modulation (BIPCM) scheme adopting 256 quadrature-amplitude modulation (256-QAM) is proposed. Moreover, a quadratic polynomial permutation (QPP) interleaver is adopted for polar coded modulation (PCM) to further improve the overall system performance. The simulation results exhibit that the proposed scheme can achieve more than 4 dB and 5 dB Q-factor improvement compared to the conventional schemes with PCM and without BIPCM, respectively. At the same time, aided by the efficient 256-QAM BIPCM scheme, the receiver sensitivity is improved and the laser linewidth requirement is less strict compared to the conventional schemes.

A BIPCM Scheme Based on OCT Precoding for a 256-QAM OFDM-VLC System

A bit-interleaved polar-coded modulation (BIPCM) scheme based on orthogonal circulant matrix transform (OCT) precoding is proposed and experimentally demonstrated in an orthogonal frequency-division multiplexing (OFDM) visible light communication system. It exhibits the advantages of high reliability, low latency, and low computational complexity. To overcome the fading effect on a mapped bit-level, the scheme employs the Monte Carlo method to jointly design a polar code concatenated with 256-ary quadrature-amplitude modulation. In addition, OCT precoding is used to mitigate the frequency selective fading effect across OFDM subcarriers. The experimental results show that the system can achieve a net data rate of 343 Mb/s over 80-cm free-space transmission with a bit error rate below $1\times 10^{-3}$ . At the receiver, it is the number of complex multiplications is reduced by 33% in comparison with BIPCM using an optimized quadratic polynomial permutation interleaver.

Joint Successive Cancellation Decoding for Bit-Interleaved Polar Coded Modulation

To improve the performance of bit-interleaved polar-coded modulation (BIPCM), a joint successive cancellation (SC) decoding algorithm for BIPCM is proposed. In the proposed algorithm, the correlation between coded bits, which are mapped into the same symbol is considered. Based on the recursive structure of the proposed algorithm, the demapping and deinterleaving units are combined with SC decoder. Thus, the information bits are directly decoded by the likelihood ratios (LRs) of the received symbols instead of the LRs of coded bits. Simulation results show that the performance of existing BIPCM schemes can be improved 0.75-1.25 dB with the proposed algorithm.