Abstract
In this work, the effect of additive white Gaussian noise and fading channel on the compressed sensing or compressive sampling (CS) image reconstruction process are demonstrated. First, the work suggests encoding of the sensed samples by low density parity check code (LDPC) before transmission. It is well known that longer is the length of the LDPC codes better (lower) is the bit error rate (BER) performance. Thus to improve CS reconstruction a method to construct a larger length but 4 cycle free irregular LDPC code structure is also proposed. The code construction is based on the LDPC code in IEEE WiMAX standard. The proposed CS-LDPC structure is then extended for \(4^n\)-QAM to find an optimal set of thresholds by minimizing BER (equivalently symbol error rate) using differential evolution (DE). The algorithm works on the log likelihood ratio values obtained by LDPC decoding. Extensive simulation results show the efficacy of the use of LDPC codes and the trade-off in code rate and measurements on reconstruction quality. Improved performance with the proposed DE based demodulation is also demonstrated.
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Donoho, D. L. (2006). Compressed sensing. IEEE Transactions on Information Theory, 52(4), 1289–1306.
Polania, L. F., Carrillo, R. E., Blanco-Velasco, M., & Barner, K. E. (2015). Exploiting prior knowledge in compressed sensing wireless ECG systems. IEEE Journal of Biomedical and Health Informatics, 19(2), 508–519.
Majumdar, A., & Ward, R. K. (2015). Energy efficient EEG sensing and transmission for wireless body area networks: A blind compressed sensing approach. Biomedical Signal Processing and Control, 20, 1–9.
Zhang, Z., Jung, T. P., Makeig, S., & Rao, B. D. (2013). Compressed sensing for energy-efficient wireless telemonitoring of noninvasive fetal ECG via block sparse Bayesian learning. IEEE Transactions on Biomedical Engineering, 60(2), 300–309.
Wang, L., Lu, K., & Liu, P. (2015). Compressed sensing of a remote sensing image based on the priors of the reference image. IEEE Geoscience and Remote Sensing Letters, 12(4), 736–740.
Li, S., Da Xu, L., & Wang, X. (2013). Compressed sensing signal and data acquisition in wireless sensor networks and internet of things. IEEE Transactions on Industrial Informatics, 9(4), 2177–2186.
Feng, L., Axel, L., Chandarana, H., Block, K. T., Sodickson, D. K., & Otazo, R. (2016). XD-GRASP: Golden-angle radial MRI with reconstruction of extra motion-state dimensions using compressed sensing. Magnetic Resonance in Medicine, 75(2), 775–788.
Zhang, Y., Zhang, L. Y., Zhou, J., Liu, L., Chen, F., & He, X. (2016). A review of compressive sensing in information security field. IEEE Access, 4, 2507–2519.
Ohlsson, H., Yang, A. Y., Dong, R., & Sastry, S. S. (2013). Nonlinear basis pursuit. In: Signals, systems and computers, 2013 Asilomar conference on IEEE (pp. 115–119).
Wang, J., Kwon, S., & Shim, B. (2012). Generalized orthogonal matching pursuit. IEEE Transactions on Signal Processing, 60(12), 6202–6216.
Yang, Z., Zhang, C., Deng, J., & Lu, W. (2011). Orthonormal expansion \(\ell _{1}\)-minimization algorithms for compressed sensing. IEEE Transactions on Signal Processing, 59(12), 6285–6290.
Egiazarian, K., Foi, A., & Katkovnik, V. (2007). Compressed sensing image reconstruction via recursive spatially adaptive filtering. In Image processing, 2007. ICIP 2007. IEEE international conference on IEEE (Vol. 1, pp. 549–I–552).
IEEE Networks, (2016). Energy-efficient dynamic traffic offloading and reconfiguration of networked data centers for big data stream mobile computing: Review, challenges, and a case study. 30(2), 54–61.
Pramanik, A., Patil, G., & Borman, L. (2013). Small length quasi-cyclic LDPC code for wireless applications. In Emerging research areas and 2013 international conference on microelectronics, communications and renewable energy (AICERA/ICMiCR), 2013 annual international conference on IEEE (pp. 1–5).
Gallager, R. (1962). Low-density parity-check codes. IRE Transactions on Information Theory, 8(1), 21–28.
Porcello, J. C. (2015). Implementing High data rate, low density parity check (LDPC) decoders for large codes using FPGAs. In Aerospace conference, 2015 IEEE (pp. 1–7).
Aimin, Z., & Senjie, Y. (2009). A modified belief propagation decoding algorithm of LDPC codes for fast convergence. In Communication software and networks, 2009. ICCSN’09. International conference on IEEE (pp. 516–520).
Healy, C. T., & de Lamare, R. C. (2016). Design of ldpc codes based on multipath emd strategies for progressive edge growth. IEEE Transactions on Communications, 64(8), 3208–3219.
Han, W., & Huang, J. (2013). A block-PEG construction method for LDPC codes. In Electronics information and emergency communication (ICEIEC), 2013 IEEE 4th international conference on IEEE (pp. 274–277).
Khodaiemehr, H., & Kiani, D. (2017). Construction and encoding of QC-LDPC codes using group rings. IEEE Transactions on Information Theory, 63(4), 2039–2060.
Zhang, J. B., Yu, Y., Chen, Z. Y., & Li, Z. Z. (2017). A new method for constructing parity check matrix of QC-LDPC codes based on shortening RS codes for wireless sensor networks. Sustainable Computing: Informatics and Systems. https://doi.org/10.1016/j.suscom.2017.09.001.
Paolini, E., Fossorier, M. P., & Chiani, M. (2010). Generalized and doubly generalized LDPC codes with random component codes for the binary erasure channel. IEEE Transactions on Information Theory, 56(4), 1651–1672.
IEEE standard. (2009). IEEE Standard for local and metropolitan area networks Part 16: Air interface for broadband wireless access systems. IEEE Std 802.16-2009 (Revision of IEEE Std 802.16-2004), 1-2080. https://doi.org/10.1109/IEEESTD.2009.5062485.
Steiner, F., Böcherer, G., & Liva, G. (2016). Protograph-based LDPC code design for shaped bit-metric decoding. IEEE Journal on Selected Areas in Communications, 34(2), 397–407.
Baron, D., Sarvotham, S., & Baraniuk, R. G. (2010). Bayesian compressive sensing via belief propagation. IEEE Transactions on Signal Processing, 58(1), 269–280.
Bayati, M., & Montanari, A. (2011). The dynamics of message passing on dense graphs, with applications to compressed sensing. IEEE Transactions on Information Theory, 57(2), 764–785.
Zhang, F., & Pfister, H. D. (2012). Verification decoding of high-rate LDPC codes with applications in compressed sensing. IEEE Transactions on Information Theory, 58(8), 5042–5058.
Akçakaya, M., Park, J., & Tarokh, V. (2011). A coding theory approach to noisy compressive sensing using low density frames. IEEE Transactions on Signal Processing, 59(11), 5369–5379.
Pham, H. V., Dai, W., & Milenkovic, O. (2009). Sublinear compressive sensing reconstruction via belief propagation decoding. In Information theory, 2009. ISIT 2009. IEEE international symposium on IEEE (pp. 674–678).
Lu, W., Kpalma, K., & Ronsin, J. (2012). Sparse binary matrices of LDPC codes for compressed sensing. In Data compression conference (DCC) (pp. 10).
Dimakis, A. G., Smarandache, R., & Vontobel, P. O. (2012). LDPC codes for compressed sensing. IEEE Transactions on Information Theory, 58(5), 3093–3114.
Chen, F., Lim, F., Abari, O., Chandrakasan, A., & Stojanovic, V. (2013). Energy-aware design of compressed sensing systems for wireless sensors under performance and reliability constraints. IEEE Transactions on Circuits and Systems I: Regular Papers, 60(3), 650–661.
Pramanik, A., & Maity, S. P. (2015). On CS reconstruction images using LDPC code over radio mobile channel. In Wireless communications, vehicular technology, information theory, aerospace and electronic systems (VITAE), 2015 5th international conference on IEEE.
Candes, E. J., Romberg, J. K., & Tao, T. (2006). Stable signal recovery from incomplete and inaccurate measurements. Communications on Pure and Applied Mathematics, 59(8), 1207–1223.
Hayashi, K., Nagahara, M., & Tanaka, T. (2013). A user’s guide to compressed sensing for communications systems. IEICE Transactions on Communications, 96(3), 685–712.
Richardson, T. J., & Urbanke, R. L. (2001). Efficient encoding of low-density parity-check codes. IEEE Transactions on Information Theory, 47(2), 638–656.
Das, S., & Suganthan, P. N. (2011). Differential evolution: A survey of the state-of-the-art. IEEE Transactions on Evolutionary Computation, 15(1), 4–31.
Qin, A. K., Huang, V. L., & Suganthan, P. N. (2009). Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Transactions on Evolutionary Computation, 13(2), 398–417.
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Pramanik, A., Maity, S.P. On CS Image Reconstruction Using LDPC Code Over Radio Mobile Channel. Wireless Pers Commun 100, 401–427 (2018). https://doi.org/10.1007/s11277-017-5079-1
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DOI: https://doi.org/10.1007/s11277-017-5079-1