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Asynchronous Polar-Coded Modulation Authors: Jincheng Dai, Kai Niu, - - PowerPoint PPT Presentation
Asynchronous Polar-Coded Modulation Authors: Jincheng Dai, Kai Niu, - - PowerPoint PPT Presentation
IEEE ISIT 2020 Asynchronous Polar-Coded Modulation Authors: Jincheng Dai, Kai Niu, and Zhongwei Si Speaker: Jincheng Dai Key Laboratory of Universal Wireless Communications, Ministry of Education Beijing University of Posts and
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Polar coding
− Polar codes achieve the capacity of binary input symmetric discrete memoryless channels (B-DMCs) under the successive cancellation (SC) decoding when the code length goes to infinity. − The key idea is “channel polarization” which comes from the chain rule of mutual information. − The channel polarization effect lies in the “coding” given by the binary constraint.
Polar-coded modulation (PCM)
− By considering the dependencies among the bits which are mapped to a single modulation symbol as a special kind of channel transform, the polar-coded modulation (PCM) scheme is derived under the framework of two-stage channel transform, i.e. the modulation partition and the binary partition. − State-of-the-art PCM framework includes two schemes, i.e. the multilevel coding (MLC) [1] and the bit-interleaved coded modulation (BICM) [2], and their corresponding PCM frameworks are referred as the MLC-PCM and the BI-PCM, respectively.
From polar coding to polar-coded modulation
Preliminaries about polar-coded modulation
[1] U. Wachsmann, R. F. H. Fischer, and J. B. Huber, “Multilevel codes: theoretical concepts and practical design rules,” IEEE Trans. Inf. Theory, vol. 45, pp. 1361–1391, Jul. 1999. [2] G. Caire, G. Taricco, and E. Biglieri, “Bit-interleaved coded modulation” IEEE Trans. Inf. Theory, vol. 44, pp. 927–946, May 1998.
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MLC-PCM
Block diagram of PCM frameworks
Preliminaries about polar-coded modulation
N-length polar code N-length polar code N-length polar code 2m-ary modulation
…
Stage 1: modulation partition Stage 2: Bit partition
QAM SP labeling with serially demodulation brings strong polarization.
BI-PCM
mN-length polar code Interleaver
Stage 1: modulation partition Stage 2: Bit partition
QAM Gray labeling with parallel demodulation brings weak polarization. 2m-ary modulation
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MLC-PCM
− For the 2m-ary quadrate amplitude modulation (QAM) methods, given N symbols to be transmitted in
- ne block, the MLC-PCM contains m component polar encoders whose code length is N.
− The MLC-PCM is capacity-achieving as N goes to infinity. − For the finite block length, the set-partition (SP) labeling rule should be adopted in QAM constellations to enhance the polarization diversity among the m modulation synthesized subchannels after the sequential partition.
BI-PCM
− Only one mN-length binary polar coding block is used, after the polar encoding and interleaving, the coded bits are mapped to the N QAM symbols. − Under the finite block length, the Gray labeling rule should be used to minimize the capacity loss during the parallel modulation partition.
Some conclusions about PCM
Preliminaries about polar-coded modulation
[1] M. Seidl, A. Schenk, C. Stierstorfer and J. B. Huber, “Polar-Coded Modulation,” IEEE Trans. Commun., vol. 61, no. 10, pp. 4108–4119, Oct. 2013.
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Backgrounds about polar-coded modulation Motivation Transmission scheme of A-PCM Channel polarization transforms in A-PCM Theoretical performance analysis Simulation results analysis and conclusion
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The shortages of MLC-PCM
− Involves m component polar codes which increase the latency. − Each component code length is N which is much shorter than the code length mN in the BI-PCM.
The shortages of BI-PCM
− The parallel modulation partition leads to the capacity loss because it does not satisfy the chain rule
- f mutual information as that in the MLC-PCM.
− The QAM with gray labeling used in BI-PCM can well reduce the capacity loss in the MLC-PCM, but the polarization effect among the modulation synthesized subchannels is much inferior to the SP labeling used in MLC-PCM.
Summary
− The MLC-PCM shows advantages on the SP labeling and no capacity loss, but its component code length is short, that makes the polarization in polar coding is insufficient for finite length N. − The BI-PCM shows advantages on the one mN-length polar code and the lower decoding latency, but its QAM labeling rule should adopt the weak polarization Gray labeling.
Motivation
Asynchronous polar-coded modulation (A-PCM)
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Can we combine the advantages of MLC-PCM and BI-PCM?
− SP labeled QAM. − One mN-length polar encoder/decoder. − Parallel modulation partition is adopted. − The strongest channel polarization effect among the modulation synthesized subchannels with no capacity loss.
Key idea
− Change the synchronous superposition mode among the bit streams to the asynchronous mode. − Introduce the spatial-coupling idea to form the modulated frame.
Motivation
Asynchronous polar-coded modulation (A-PCM)
1001 0111 1010 0100 0011 1101 0000 1110 0110 1100 1000 0010 0101 1111 1011 0001 Q I 1001 0111 1010 0100 0011 1101 0000 1110 0110 1100 1000 0010 0101 1111 1011 0001 Q I 1001 0111 1010 0100 0011 1101 0000 1110 0110 1100 1000 0010 0101 1111 1011 0001 Q I 1001 0111 1010 0100 0011 1101 0000 1110 0110 1100 1000 0010 0101 1111 1011 0001 Q I
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Why the “well-polarized” SP labeling cannot be used for BI-PCM?
− The existing PCM frameworks are indeed the synchronous schemes where the N transmitted 2m-ary symbols in each frame come from one coded block. Hence, the interference among the modulation bit streams is severe. − The parallel modulation partition in BI-PCM leads to capacity loss which makes the “well-polarized” SP labeling in MLC-PCM cannot be used.
A-PCM combines the advantages of MLC-PCM and BI-PCM
− We propose an asynchronous PCM (A-PCM) framework, where the N transmitted 2m-ary symbols in each frame comes from m different coded blocks. − The coded bits in one block are asynchronously transmitted within m frames, and various coded blocks form the spatial coupled structure. − Although the parallel demodulation in BICM scheme is used, the previous m − 1 decoded blocks will mitigate the interference among the modulation bit streams so that the SP labeling can be used with no capacity loss during the parallel modulation partition.
Key idea of A-PCM
Asynchronous polar-coded modulation (A-PCM)
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Backgrounds about polar-coded modulation Motivation Transmission scheme of A-PCM Channel polarization transforms in A-PCM Theoretical performance analysis Simulation results analysis and conclusion
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− Only one mN-length polar encoder is utilized for one block, and m coded blocks are superposed as the spatial-coupled structure. − The coded bits in each block is divided to m segments, and each segment is mapped to different frames and different bits.
Transmission scheme
A-PCM transmission scheme
...
Transmitted Frames Polar Coded Blocks 1 2 3 4
...
4-ary 8-ary 16-ary 16-ary 16-ary
... ...
16-ary 16-ary
Modulation to one frame
2-ary
1 2 3 4
...
Bit-4 Bit-3 Bit-2 Bit-1
in BI-PCM
Bit-1 in the ( 3)-th frame t + Bit-2 in the ( 2)-th frame t + Bit-3 in the ( 1)-th frame t + Bit-4 in the -th frame t
The capacity distribution is the same as that with SP labeling in MLC-PCM. Nested structure
- f polar codes
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Transmission scheme
A-PCM transmission scheme
...
Transmitted Frames Polar Coded Blocks 1 2 3 4
...
4-ary 8-ary 16-ary 16-ary 16-ary
... ...
16-ary 16-ary
Modulation to one frame
2-ary
1 2 3 4
...
Bit-4 Bit-3 Bit-2 Bit-1
No interference! Equivalent to a 2-ary modulation.
1001 0111 1010 0100 0011 1101 0000 1110 0110 1100 1000 0010 0101 1111 1011 0001 Q I
0/1
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Transmission scheme
A-PCM transmission scheme
...
Transmitted Frames Polar Coded Blocks 1 2 3 4
...
4-ary 8-ary 16-ary 16-ary 16-ary
... ...
16-ary 16-ary
Modulation to one frame
2-ary
1 2 3 4
...
Bit-4 Bit-3 Bit-2 Bit-1
0/1 0/1
1001 0111 1010 0100 0011 1101 0000 1110 0110 1100 1000 0010 0101 1111 1011 0001 Q I
Due to interference mitigation, the parallel demodulation in this frame is equivalent to the serial demodulation in MLC-PCM.
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Transmission scheme
A-PCM transmission scheme
...
Transmitted Frames Polar Coded Blocks 1 2 3 4
...
4-ary 8-ary 16-ary 16-ary 16-ary
... ...
16-ary 16-ary
Modulation to one frame
2-ary
1 2 3 4
...
Bit-4 Bit-3 Bit-2 Bit-1
0/1 0/1 0/1
1001 0111 1010 0100 0011 1101 0000 1110 0110 1100 1000 0010 0101 1111 1011 0001 Q I
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Transmission scheme
A-PCM transmission scheme
...
Transmitted Frames Polar Coded Blocks 1 2 3 4
...
4-ary 8-ary 16-ary 16-ary 16-ary
... ...
16-ary 16-ary
Modulation to one frame
2-ary
1 2 3 4
...
Bit-4 Bit-3 Bit-2 Bit-1
1001 0111 1010 0100 0011 1101 0000 1110 0110 1100 1000 0010 0101 1111 1011 0001 Q I
0/1 0/1 0/1 0/1
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Backgrounds about polar-coded modulation Motivation Transmission scheme of A-PCM Channel polarization transforms in A-PCM Theoretical performance analysis Simulation results analysis and conclusion
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Stage 1: modulation partition
− Let denote a discrete memoryless channel (DMC) with input symbols. Given the m-bit sequence, the order-m modulation partition (MP) in the asynchronous PCM is characterized as L, which maps W to an ordered set of binary memoryless channels (BMCs) Wk with k = 1, 2, · · · , m, which are referred as the modulation synthesized subchannels. From the mutual information perspective, we have which indicates the stage 1 partition preserves the capacity.
Stage 2: bit partition
− The second stage performs an mN-dimensional channel polarization transform GmN on N groups of {Wk}, and the resulting BMCs {W(i)
mN} with indices i = 1, 2, · · · ,mN are referred as the bit polarized
subchannels.
Channel transforms in A-PCM
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Virtually demonstration about the two-stage channel transform
Channel transforms in A-PCM
groups Step 1 Step 2 Stage 1: modulation partition Stage 2: bit partition The capacity distribution is the same as that in the MLC-PCM (QAM with SP labeling).
Polarization enhancement
Conventional polar coding. Contribute to the performance gain of A-PCM.
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Backgrounds about polar-coded modulation Motivation Transmission scheme of A-PCM Channel polarization transforms in A-PCM Theoretical performance analysis Simulation results analysis and conclusion
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Capacity achieving under the infinite frame length
− The asynchronous PCM is capacity-achieving as N goes to infinity. Proof: Followed by the capacity-achieving property of polar codes, as N goes to infinity, it can be inferred that which indicates the asynchronous PCM is capacity-achieving under the infinite block length.
Performance analysis of A-PCM
Performance analysis under the finite frame length
− For the finite frame length N, the final polarization diversity among the bit polarized subchannels can be characterized with the mean and variance, defined respectively as
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Performance analysis of A-PCM
Proposition
− Compared to the MLC-PCM and BI-PCM, the final bit polarized subchannels {W(i)
mN} in the
asynchronous PCM can be more sufficiently polarized under the finite frame length N , i.e. we have − In summary, the asynchronous PCM could bring enhanced polarization superiority over the MLC-PCM and the BI-PCM under the finite frame length N. As the frame length goes to infinity (N → +∞), the MLC-PCM and the asynchronous PCM converge to the identical capacity-achieving performance, the BI-PCM yet presents degradation due to the capacity loss in the modulation partition step.
Capacity mean of MLC- PCM with the SP labeling Capacity mean of BI-PCM with the Gray labeling Capacity variance of MLC- PCM with the SP labeling Capacity variance of BI- PCM with the Gray labeling
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Performance analysis of A-PCM
Main observations
− The A-PCM brings better polarization diversity with respect to the MLC-PCM and the BI-PCM so that the relative variance stays positive. − Also, the increasing of frame length N results in the reduction on the relative variance. − This verifies the conclusion that as N goes to infinity, the A-PCM and the MLC-PCM tends to the same capacity-achieving performance.
256QAM 64QAM
A-PCM vs BI-PCM A-PCM vs MLC-PCM A-PCM vs BI-PCM A-PCM vs MLC-PCM
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Backgrounds about polar-coded modulation Motivation Transmission scheme of A-PCM Channel polarization transforms in A-PCM Theoretical performance analysis Simulation results analysis and conclusion
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Performance evaluation results
Simulation configurations
− We compare the block-error-ratio (BLER) performance with various coded modulation schemes over the additive white Gaussian noise (AWGN) channel. − The frame length is set to N = 128, and the coding rate is R = 0.5. The 64QAM and 256QAM modulation are adopted. − The cyclic-redundancy-check (CRC) aided SCL (CA-SCL) algorithm with the 16-bit CRC sequence and list size L = 32 is used for each block decoding. − Regarding the LDPC coded modulation (LCM) schemes, the LDPC code construction follows the 5G standard, and the LDPC decoding uses the layered sum-product-algorithm (SPA) with 20 iterations
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Performance evaluation results
Results analysis
− The proposed A-PCM outperforms the conventional MLC-PCM and BI-PCM especially for the high signal-to-noise-ratio (SNR) regimes. − Also, we note that the BLER curve of the A- PCM shows the slop gain compared to the MLC-PCM and the BI-PCM. It indicates the A-PCM wins the extra coding gain by the enhanced polarization diversity among the bit polarized subchannels. − As for the cost of A-PCM, the decoding complexity is identical as that in the BI-PCM, but A-PCM needs to receive m frames data to complete the demodulation and decoding, which corresponds to higher latency.
64QAM 256QAM
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Conclusion and future trends
Conclusion
− In this paper, inspired by spatial-coupling idea, we design an asynchronous PCM framework which allows for enhanced polarization diversity under the finite length. Theoretical analysis and simulation results prove the superiority with respect to state-of-the-art PCM schemes.
Future trends
− To improve the performance of polar-coded system, the most efficient way is to enhance the polarization diversity gain, i.e., the polarization effect among the final bit polarized subchannels. − For more complex systems, e.g., the polar-coded MIMO etc., one can also asynchronously transmit the data streams, in this way, the interference can be well mitigated. Also, the seemingly “parallel” detection/demodulation can lead to the well-polarized serially detection/demodulation results.
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