Adaptive BitLabeling Design for Probabilistic Shaping Based on Residual Source Redundancy
Abstract
:1. Introduction
 By studying the effects of bitlabeling in JSCCM systems, it is found that good bitlabelings for different source codes or different source probabilities could be different.
 Based on the achievable system rate analysis, a new shaping scheme for the JSCCM system is proposed by optimizing the bitlabeling.
 In contrast to the fixed Gray labeling [16], the adaptive design of bitlabelings for the JSCCM system is proposed according to the source codes and the source probabilities. Since it is much simpler to switch between labelings than to optimize the sourcechannel code pairs for different source probabilities, it is attractive for systems with changing source statistics.
2. System Model
3. Analysis and Design of BitLabeling
3.1. Effects of BitLabelings
3.2. An Adaptive Design Scheme of BitLabeling
Algorithm 1 Adaptive BitLabeling Design 
Require: $p,{B}_{s},R,\mathsf{\Delta},{\varphi}_{ini}$

4. Experimental Results
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
AWGN  Additive white Gaussian noise 
BER  Bit error rate 
BICM  Bit interleaved coded modulation 
DM  Distribution matcher 
JSCC  Joint sourcechannel coding 
JSCCM  Joint sourcechannel coded modulation 
PAS  Probabilistic amplitude shaping 
PEG  Progressive edge growth 
QAM  Quadrature amplitude modulation 
References
 Caire, G.; Taricco, G.; Biglieri, E. Bitinterleaved coded modulation. IEEE Trans. Inf. Theory 1998, 3, 927–946. [Google Scholar] [CrossRef][Green Version]
 Forney, G.D.; Gallager, R.G.; Lang, G.; Longstaff, F.; Qureshi, S. Efficient modulation for bandlimited channels. IEEE J. Sel. Areas Commun. 1984, 5, 632–647. [Google Scholar] [CrossRef][Green Version]
 Böcherer, G.; Steiner, F.; Schulte, P. Bandwidth efficient and ratematched lowdensity paritycheck coded modulation. IEEE Trans. Commun. 2015, 12, 4651–4665. [Google Scholar] [CrossRef][Green Version]
 Steiner, F.; Böcherer, G.; Liva, G. Bitmetric decoding of nonbinary LDPC codes with probabilistic amplitude shaping. IEEE Commun. Lett. 2018, 11, 2210–2213. [Google Scholar] [CrossRef][Green Version]
 Steiner, F.; Böcherer, G.; Liva, G. Protographbased LDPC code design for shaped bitmetric decoding. IEEE J. Sel. Areas Commun. 2016, 2, 397–407. [Google Scholar] [CrossRef][Green Version]
 Corlay, V.; Gresset, N. A simple signbit probabilistic shaping scheme. IEEE Commun. Lett. 2022, 4, 763–767. [Google Scholar] [CrossRef]
 Kang, W. A probabilistic shaping scheme for bitinterleaved coded modulation with iterative decoding. IEEE Commun. Lett. 2022, 11, 2517–2521. [Google Scholar] [CrossRef]
 Schulte, P.; Böcherer, G. Constant composition distribution matching. IEEE Trans. Inf. Theory. 2016, 62, 1–5. [Google Scholar] [CrossRef][Green Version]
 Perkert, R.; Kaindl, M.; Hindelang, T. Iterative source and channel decoding for GSM. In Proceedings of the IEEE ICASSP, Salt Lake City, UT, USA, 7–11 May 2001; pp. 2649–2652. [Google Scholar]
 Othman, N.S.; ElHajjar, M.; Alamri, O.; Hanzo, L. Softbit assisted iterative AMRWB sourcedecoding and turbodetection of channelcoded differential spacetime spreading using sphere packing modulation. In Proceedings of the IEEE VTCSpring, Dublin, Ireland, 22–25 April 2007; pp. 2010–2014. [Google Scholar]
 Kliewer, J.; Gortz, N. Iterative sourcechannel decoding for robust image transmission. In Proceedings of the IEEE ICASSP, Orlando, FL, USA, 13–17 May 2002; pp. 2173–2176. [Google Scholar]
 Zhu, G.; Alajaji, F. Joint SourceChannel Turbo Coding for Binary Markov Sources. IEEE Trans. Signal Process. 2006, 5, 1065–1075. [Google Scholar]
 Nasruminallah; ElHajjar, M.; Othman, N.S.; Quang, A.P.; Hanzo, L. Overcomplete mapping aided, softbit assisted iterative unequal error protection H.264 joint source and channel decoding. In Proceedings of the IEEE VTCFall, Calgary, AB, Canada, 21–24 September 2008; pp. 1–5. [Google Scholar]
 Chen, Q.; He, Y.; Chen, C.; Zhou, L. Optimization of protograph LDPC codes via surrogate channel for unequal power allocation. IEEE Trans. Commun. 2023. early access. [Google Scholar] [CrossRef]
 Chen, C.; Chen, Q.; Wang, L.; He, Y.C.; Chen, Y. Probabilistic shaping for protograph LDPCcoded modulation by residual source redundancy. IEEE Trans. Commun. 2021, 7, 4267–4281. [Google Scholar] [CrossRef]
 Agrell, E.; Lassing, J.; Ström, E.G.; Ottosson, T. On the optimality of the binary reflected Gray code. IEEE Trans. Inf. Theory 2004, 12, 3170–3182. [Google Scholar] [CrossRef]
 Nguyen, V. Design of CapacityApproaching ProtographBased LDPC Coding Systems. Ph.D. Dissertation, University of Texas at Dallas, Dallas, TX, USA, December 2012. [Google Scholar]
 He, J.; Li, Y.; Wu, G.; Qian, S.; Xue, Q.; Matsumoto, T. Performance improvement of joint sourcechannel coding with unequal power allocation. IEEE Wirel. Commun. Lett. 2017, 5, 582–585. [Google Scholar] [CrossRef][Green Version]
 Divsalar, D.; Dolinar, S.; Jones, C.R.; Andrews, K. Capacity approaching protograph codes. IEEE J. Sel. Areas. Commun. 2009, 6, 876–888. [Google Scholar] [CrossRef]
 Chen, C.; Wang, L.; Lau, F.C.M. Joint optimization of protpgraph LDPC code pair for joint source and channel coding. IEEE Trans. Commun. 2018, 8, 3255–3267. [Google Scholar] [CrossRef]
 Uchikawa, H. Design of nonprecoded protographbased LDPC codes. In Proceedings of the IEEE International Symposium on Information Theory (ISIT), Honolulu, HI, USA, 29 June–4 July 2014; pp. 2779–2783. [Google Scholar]
 Chen, Q.; Wang, L. Design and Analysis of Joint Source Channel Coding Schemes Over NonStandard Coding Channels. IEEE Trans. Veh. Technol. 2020, 5, 5369–5380. [Google Scholar] [CrossRef]
 Lyu, Y.; Wang, L.; Cai, G.; Chen, G. Iterative receiver for Mary DCSK systems. IEEE Trans. Commun. 2015, 11, 3929–3936. [Google Scholar] [CrossRef]
Source Probability  Source Code  Target Rate (Bits/Symbol)  Optimized Labeling 

$p=0.05$  ${\mathbf{B}}^{s,1}$  6  ${L}_{opt1}$ 
$p=0.05$  ${\mathbf{B}}^{R4JA}$  6  ${L}_{opt2}$ 
$p=0.03$  ${\mathbf{B}}^{s,2}$  8  ${L}_{opt3}$ 
$p=0.03$  ${\mathbf{B}}^{s,3}$  8  ${L}_{opt2}$ 
$p=0.94$  ${\mathbf{B}}^{s,1}$  6  ${L}_{opt4}$ 
$p=0.94$  ${\mathbf{B}}^{R4JA}$  6  ${L}_{opt2}$ 
$p=0.98$  ${\mathbf{B}}^{s,2}$  8  ${L}_{opt5}$ 
$p=0.98$  ${\mathbf{B}}^{s,3}$  8  ${L}_{opt6}$ 
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. 
© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Chen, C.; Chen, Q.; Liu, S.; Zhou, L. Adaptive BitLabeling Design for Probabilistic Shaping Based on Residual Source Redundancy. Entropy 2023, 25, 586. https://doi.org/10.3390/e25040586
Chen C, Chen Q, Liu S, Zhou L. Adaptive BitLabeling Design for Probabilistic Shaping Based on Residual Source Redundancy. Entropy. 2023; 25(4):586. https://doi.org/10.3390/e25040586
Chicago/Turabian StyleChen, Chen, Qiwang Chen, Sanya Liu, and Lin Zhou. 2023. "Adaptive BitLabeling Design for Probabilistic Shaping Based on Residual Source Redundancy" Entropy 25, no. 4: 586. https://doi.org/10.3390/e25040586