The Efficient Design of Lossy P-LDPC Codes over AWGN Channels
Abstract
:1. Introduction
- 1.
- The connection between and the total degree of the variable nodes of a protomatrix is derived and experimentally verified.
- 2.
- Two optimization algorithms are proposed based on the principle of balanced degree allocation, and the optimized codes have excellent compression performance and error resilience.
2. System Model
3. Analysis and Optimization Methods
3.1. Analysis for Low SNR Region
3.2. Optimization for High SNR Region
Algorithm 1 CA algorithm and CVA algorithm |
Require: AR3A-impr codes and AR4JA-impr codes [11] Ensure: CA-AR3A-impr codes and CVA-AR3A-impr codes; CA-AR4JA-impr codes and CVA-AR4JA-impr codes.
|
Algorithm 2 GDA algorithm |
Require: M & N & d; Ensure: GDA codes
|
4. Simulation Results and Analysis
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
- Shannon, C.E. A mathematical theory of communication. Bell Syst. Tech. J. 1948, 27, 379–423. [Google Scholar] [CrossRef] [Green Version]
- Shannon, C.E. Communication in the presence of noise. Proc. IEEE 1998, 86, 447–457. [Google Scholar] [CrossRef]
- Gupta, A.; Verdu, S. Operational duality between lossy compression and channel coding. IEEE Trans. Inf. Theory 2011, 57, 3171–3179. [Google Scholar] [CrossRef]
- Chen, D. On two or more dimensional optimum quantizers. In Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing, Hartford, CT, USA, 9–11 May 1977; pp. 640–643. [Google Scholar]
- Matsunaga, Y.; Yamamoto, H. A coding theorem for lossy data compression by LDPC codes. IEEE Trans. Inf. Theory 2003, 49, 2225–2229. [Google Scholar] [CrossRef] [Green Version]
- Martinian, E.; Wainwright, M. Low density codes achieve the distortion rate bound. In Proceedings of the Data Compression Conference (DCC’06), Snowbird, UT, USA, 28–30 March 2006; pp. 153–162. [Google Scholar]
- Wainwright, M.J.; Maneva, E.; Martinian, E. Lossy source compression using low-density generator matrix codes: Analysis and algorithms. IEEE Trans. Inf. Theory 2010, 56, 1351–1368. [Google Scholar] [CrossRef] [Green Version]
- Wainwright, M.J.; Maneva, E. Lossy source encoding via message-passing and decimation over generalized codewords of LDGM codes. In Proceedings of the International Symposium on Information Theory, Adelaide, SA, Australia, 4–9 September 2005; pp. 1493–1497. [Google Scholar]
- Nguyen, T.V.; Nosratinia, A.; Divsalar, D. The design of rate-compatible protograph LDPC codes. IEEE Trans. Commun. 2012, 60, 2841–2850. [Google Scholar] [CrossRef]
- Hu, X.Y.; Eleftheriou, E.; Arnold, D.M. Regular and irregular progressive edge-growth tanner graphs. IEEE Trans. Inf. Theory 2005, 51, 386–398. [Google Scholar] [CrossRef]
- Liu, S. Research on the Design Principles of Joint Coding and Lossy Source Coding System Based on P-LDPC Codes. Ph.D. Thesis, Xiamen University, Xiamen, China, 2021. [Google Scholar]
- Braunstein, A.; Kayhan, F.; Montorsi, G.; Zecchina, R. Encoding for the blackwell channel with reinforced belief propagation. In Proceedings of the 2007 IEEE International Symposium on Information Theory, Nice, France, 24–29 June 2007; pp. 1891–1895. [Google Scholar]
- Gray, R. Vector quantization. IEEE ASSP Mag. 1984, 1, 4–29. [Google Scholar] [CrossRef]
- Linde, Y.; Buzo, A.; Gray, R. An algorithm for vector quantizer design. IEEE Trans. Commun. 1980, 28, 84–95. [Google Scholar] [CrossRef] [Green Version]
- Farvardin, N. A study of vector quantization for noisy channels. IEEE Trans. Inf. Theory 1990, 36, 799–809. [Google Scholar] [CrossRef]
- Skoglund, M. Optimal and sub-optimal decoding for vector quantization over noisy channels with memory. In Proceedings of the 9th European Signal Processing Conference (EUSIPCO 1998), Rhodes, Greece, 8–11 September 1998; pp. 1–4. [Google Scholar]
- Chang, W.W.; Hsu, H.I. Robust vector quantization for channels with memory. In Proceedings of the 2001 IEEE International Symposium on Information Theory (IEEE Cat. No.01CH37252), Washington, DC, USA, 24–29 June 2001; p. 239. [Google Scholar]
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Wang, R.; Liu, S.; Wu, H.; Wang, L. The Efficient Design of Lossy P-LDPC Codes over AWGN Channels. Electronics 2022, 11, 3337. https://doi.org/10.3390/electronics11203337
Wang R, Liu S, Wu H, Wang L. The Efficient Design of Lossy P-LDPC Codes over AWGN Channels. Electronics. 2022; 11(20):3337. https://doi.org/10.3390/electronics11203337
Chicago/Turabian StyleWang, Runfeng, Sanya Liu, Huihui Wu, and Lin Wang. 2022. "The Efficient Design of Lossy P-LDPC Codes over AWGN Channels" Electronics 11, no. 20: 3337. https://doi.org/10.3390/electronics11203337
APA StyleWang, R., Liu, S., Wu, H., & Wang, L. (2022). The Efficient Design of Lossy P-LDPC Codes over AWGN Channels. Electronics, 11(20), 3337. https://doi.org/10.3390/electronics11203337