Research Article
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Layered Encoding With Galois Fourier Transform For Burst Erasure Recovery In Distributed Cloud Storage Systems

Year 2026, Volume: 9 Issue: 1, 147 - 157, 15.01.2026
https://doi.org/10.34248/bsengineering.1780039
https://izlik.org/JA64BJ53GB

Abstract

Burst erasures caused by rack level failures, correlated hardware faults, and network partitions challenge the reliability of distributed cloud storage. This article presents a Galois Fourier Transform (GFT) layered encoding of data which is more resistance to these failures and prioritizes the recovery of more important data. The method uses a two layer encoding structure, dividing data into base and enhancement layer. It uses GFT to encode symbols based on the efficiency in the number of nodes. To address burst erasures, a decoder which adaptively recovers base from the preserved encoded fragments is presented. Simulations show that the proposed adaptive decoder method recovers the base layer through severe bursts of the preserved enhanced layer. Therefore, it reveals that field transforms redundancy and operates as a low overhead, priority aware coding solution for future cloud storage systems.

Ethical Statement

Ethics committee approval was not required for this study because of there was no study on animals or humans.

References

  • Alzahrani, A., Alyas, T., Alissa, K., Abbas, Q., Alsaawy, Y., & Tabassum, N. (2022). Hybrid approach for improving the performance of data reliability in cloud storage management. Sensors, 22(15), 5966. https://doi.org/10.3390/s22165966
  • Bakirov, A., Matrassulova, D., Vitulyova, Y., & Auyezov, A. (2024). The specifics of the Galois field GF(257) and its use for digital signal processing. Scientific Reports, 14(1), 15376. https://doi.org/10.1038/s41598-024-66332-2
  • Blahut, R. E. (1983). Theory and practice of error control codes. Addison-Wesley.
  • Blahut, R. E. (2003). Algebraic codes for data transmission. Cambridge University Press.
  • Edward, S., & Tony, W. (2020). Building matrices with prescribed size and number of invertible submatrices. European Journal of Combinatorics, 83, 103016. https://doi.org/10.1016/j.ejc.2019.103016
  • Farkaš, P., & Rakús, M. (2023). Run length limited error control codes derived from reed solomon codes. Wireless Personal Communications, 133(1), 795–810. https://doi.org/10.1007/s11277-023-10791-9
  • Gao, S. (2003). A new algorithm for decoding Reed-Solomon codes. In Communications, Information and Network Security (The Springer International Series in Engineering and Computer Science, Vol. 712). Springer. https://doi.org/10.1007/978-1-4757-3789-9_5
  • Gordon, G. M. (1976). Very simple method to find the minimum polynomial of an arbitrary nonzero element of a finite field. Electronics Letters, 12(24), 663–664.
  • Hostetter, M. (2020). Galois: A performant NumPy extension for Galois fields. https://github.com/mhostetter/galois
  • Hou, H., Shum, K. W., Chen, M., & Li, H. (2016). BASIC codes: low-complexity regenerating codes for distributed storage systems. IEEE Transactions on Information Theory, 62(6), 3053–3069. https://doi.org/10.1109/TIT.2016.2553670
  • Khan, A. Q., Matskin, M., Prodan, R., & Waseem, H. (2024). Cloud storage tier optimization through storage object classification. Computing, 106(12), 3389–3418. https://doi.org/10.1007/s00607-024-01281-2
  • Maxime, G., Dante, D., Sanchez, G., Haochen, P., Bogdan, N., Sicheng, Z., Hai, D., Valerie, H., Greg, P., Jesus, C., Kyle, C., & Ian, F. (2025). D-Rex: Heterogeneity-aware reliability framework and adaptive algorithms for distributed storage. In Proceedings of the 39th ACM International Conference on Supercomputing (ICS '25) (pp. 853–867). Association for Computing Machinery. https://doi.org/10.1145/3721145.3730412
  • Mingyu L, Li P, Shijun L. 2022. Effeclouds: A cost-effective cloud-of-clouds framework for two-tier storage. Future Gener Comput Syst, 129: 33-49, ISSN 0167-739X, https://doi.org/10.1016/j.future.2021.11.012
  • Ong, K. L. (2023). Burst error-correcting quantum stabilizer codes designed from idempotents. Quantum Information Processing, 22(4), 158. https://doi.org/10.1007/s11128-023-03904-7
  • Oppenheim, A. V., & Schafer, R. W. (2010). Discrete-time signal processing (3rd ed.). Pearson Print.
  • Rashimi, K., Ali, S. A., Padmanabhan, B., & Vinod, V. (2011). Optimal exact-regenerating codes for distributed storage at the MSR and MBR points via a product-matrix construction. IEEE Transactions on Information Theory, 57(8), 5227–5239. https://doi.org/10.1109/TIT.2011.2159049
  • Reed, I. S., & Solomon, G. (1960). Polynomial codes over certain finite fields. Journal of the Society for Industrial and Applied Mathematics, 8(2), 300–304. http://dx.doi.org/10.1137/0108018
  • Shu, L., & Costello Jr., D. J. (2004). Error control coding (2nd ed.). Pearson.
  • Tian, C., Sasidharan, B., Aggarwal, V., Vaishampayan, V., & Kumar, P. (2015). Layered exact-repair regenerating codes via embedded error correction and block designs. IEEE Transactions on Information Theory, 61(4), 1933–1947. https://doi.org/10.1109/TIT.2015.2408595
  • Tianli, Z., & Chao, T. (2020). Fast erasure coding for data storage: a comprehensive study of the acceleration techniques. ACM Transactions on Storage, 16(1), 1.
  • Tsai, Q., Shao, E., Elston, J., & W, T. (2010). Prioritizing service requests on cloud with multi-tenancy. In IEEE 7th International Conference on E-Business Engineering (pp. 117–124). Shanghai, China: IEEE. https://doi.org/10.1109/ICEBE.2010.38
  • Tu, Y., Xiao, R., Han, Y., Chen, Y., Yu, D., & Yang, B. (2023). DDUC: an erasure-coded system with decoupled data updating and coding. Frontiers of Information Technology & Electronic Engineering, 24(5), 716–730. https://doi.org/10.1631/FITEE.2200466
  • Wu, X., Wang, Y., & Yan, Z. (2012). On algorithms and complexities of cyclotomic fast fourier transforms over arbitrary finite fields. IEEE Transactions on Signal Processing, 60(3), 1149–1158. https://doi.org/10.1109/TSP.2011.2178844
  • Xiao, Y., Zhou, S., & Zhong, L. (2020). Erasure coding-oriented data update for cloud storage: A survey. IEEE Access, 8, 227982–227998.
  • Zhang, X., Cai, Y., Liu, Y., Zhao, Y., Deng, M., Cui, B., & Hu, M. (2020). NADE: nodes performance awareness and accurate distance evaluation for degraded read in heterogeneous distributed erasure code-based storage. Journal of Supercomputing, 76(6), 4946–4975. https://doi.org/10.1007/s11227-019-02879-6
  • Zhen, H., Jinbang, C., Yisong, L., Pengfei, Y., & Yuxing, P. (2015). Minimizing data redundancy for high reliable cloud storage systems. Computer Networks, 81, 164–177. https://doi.org/10.1016/j.comnet.2015.02.013

Layered Encoding With Galois Fourier Transform For Burst Erasure Recovery In Distributed Cloud Storage Systems

Year 2026, Volume: 9 Issue: 1, 147 - 157, 15.01.2026
https://doi.org/10.34248/bsengineering.1780039
https://izlik.org/JA64BJ53GB

Abstract

Burst erasures caused by rack level failures, correlated hardware faults, and network partitions challenge the reliability of distributed cloud storage. This article presents a Galois Fourier Transform (GFT) layered encoding of data which is more resistance to these failures and prioritizes the recovery of more important data. The method uses a two layer encoding structure, dividing data into base and enhancement layer. It uses GFT to encode symbols based on the efficiency in the number of nodes. To address burst erasures, a decoder which adaptively recovers base from the preserved encoded fragments is presented. Simulations show that the proposed adaptive decoder method recovers the base layer through severe bursts of the preserved enhanced layer. Therefore, it reveals that field transforms redundancy and operates as a low overhead, priority aware coding solution for future cloud storage systems.

Ethical Statement

Ethics committee approval was not required for this study because of there was no study on animals or humans.

References

  • Alzahrani, A., Alyas, T., Alissa, K., Abbas, Q., Alsaawy, Y., & Tabassum, N. (2022). Hybrid approach for improving the performance of data reliability in cloud storage management. Sensors, 22(15), 5966. https://doi.org/10.3390/s22165966
  • Bakirov, A., Matrassulova, D., Vitulyova, Y., & Auyezov, A. (2024). The specifics of the Galois field GF(257) and its use for digital signal processing. Scientific Reports, 14(1), 15376. https://doi.org/10.1038/s41598-024-66332-2
  • Blahut, R. E. (1983). Theory and practice of error control codes. Addison-Wesley.
  • Blahut, R. E. (2003). Algebraic codes for data transmission. Cambridge University Press.
  • Edward, S., & Tony, W. (2020). Building matrices with prescribed size and number of invertible submatrices. European Journal of Combinatorics, 83, 103016. https://doi.org/10.1016/j.ejc.2019.103016
  • Farkaš, P., & Rakús, M. (2023). Run length limited error control codes derived from reed solomon codes. Wireless Personal Communications, 133(1), 795–810. https://doi.org/10.1007/s11277-023-10791-9
  • Gao, S. (2003). A new algorithm for decoding Reed-Solomon codes. In Communications, Information and Network Security (The Springer International Series in Engineering and Computer Science, Vol. 712). Springer. https://doi.org/10.1007/978-1-4757-3789-9_5
  • Gordon, G. M. (1976). Very simple method to find the minimum polynomial of an arbitrary nonzero element of a finite field. Electronics Letters, 12(24), 663–664.
  • Hostetter, M. (2020). Galois: A performant NumPy extension for Galois fields. https://github.com/mhostetter/galois
  • Hou, H., Shum, K. W., Chen, M., & Li, H. (2016). BASIC codes: low-complexity regenerating codes for distributed storage systems. IEEE Transactions on Information Theory, 62(6), 3053–3069. https://doi.org/10.1109/TIT.2016.2553670
  • Khan, A. Q., Matskin, M., Prodan, R., & Waseem, H. (2024). Cloud storage tier optimization through storage object classification. Computing, 106(12), 3389–3418. https://doi.org/10.1007/s00607-024-01281-2
  • Maxime, G., Dante, D., Sanchez, G., Haochen, P., Bogdan, N., Sicheng, Z., Hai, D., Valerie, H., Greg, P., Jesus, C., Kyle, C., & Ian, F. (2025). D-Rex: Heterogeneity-aware reliability framework and adaptive algorithms for distributed storage. In Proceedings of the 39th ACM International Conference on Supercomputing (ICS '25) (pp. 853–867). Association for Computing Machinery. https://doi.org/10.1145/3721145.3730412
  • Mingyu L, Li P, Shijun L. 2022. Effeclouds: A cost-effective cloud-of-clouds framework for two-tier storage. Future Gener Comput Syst, 129: 33-49, ISSN 0167-739X, https://doi.org/10.1016/j.future.2021.11.012
  • Ong, K. L. (2023). Burst error-correcting quantum stabilizer codes designed from idempotents. Quantum Information Processing, 22(4), 158. https://doi.org/10.1007/s11128-023-03904-7
  • Oppenheim, A. V., & Schafer, R. W. (2010). Discrete-time signal processing (3rd ed.). Pearson Print.
  • Rashimi, K., Ali, S. A., Padmanabhan, B., & Vinod, V. (2011). Optimal exact-regenerating codes for distributed storage at the MSR and MBR points via a product-matrix construction. IEEE Transactions on Information Theory, 57(8), 5227–5239. https://doi.org/10.1109/TIT.2011.2159049
  • Reed, I. S., & Solomon, G. (1960). Polynomial codes over certain finite fields. Journal of the Society for Industrial and Applied Mathematics, 8(2), 300–304. http://dx.doi.org/10.1137/0108018
  • Shu, L., & Costello Jr., D. J. (2004). Error control coding (2nd ed.). Pearson.
  • Tian, C., Sasidharan, B., Aggarwal, V., Vaishampayan, V., & Kumar, P. (2015). Layered exact-repair regenerating codes via embedded error correction and block designs. IEEE Transactions on Information Theory, 61(4), 1933–1947. https://doi.org/10.1109/TIT.2015.2408595
  • Tianli, Z., & Chao, T. (2020). Fast erasure coding for data storage: a comprehensive study of the acceleration techniques. ACM Transactions on Storage, 16(1), 1.
  • Tsai, Q., Shao, E., Elston, J., & W, T. (2010). Prioritizing service requests on cloud with multi-tenancy. In IEEE 7th International Conference on E-Business Engineering (pp. 117–124). Shanghai, China: IEEE. https://doi.org/10.1109/ICEBE.2010.38
  • Tu, Y., Xiao, R., Han, Y., Chen, Y., Yu, D., & Yang, B. (2023). DDUC: an erasure-coded system with decoupled data updating and coding. Frontiers of Information Technology & Electronic Engineering, 24(5), 716–730. https://doi.org/10.1631/FITEE.2200466
  • Wu, X., Wang, Y., & Yan, Z. (2012). On algorithms and complexities of cyclotomic fast fourier transforms over arbitrary finite fields. IEEE Transactions on Signal Processing, 60(3), 1149–1158. https://doi.org/10.1109/TSP.2011.2178844
  • Xiao, Y., Zhou, S., & Zhong, L. (2020). Erasure coding-oriented data update for cloud storage: A survey. IEEE Access, 8, 227982–227998.
  • Zhang, X., Cai, Y., Liu, Y., Zhao, Y., Deng, M., Cui, B., & Hu, M. (2020). NADE: nodes performance awareness and accurate distance evaluation for degraded read in heterogeneous distributed erasure code-based storage. Journal of Supercomputing, 76(6), 4946–4975. https://doi.org/10.1007/s11227-019-02879-6
  • Zhen, H., Jinbang, C., Yisong, L., Pengfei, Y., & Yuxing, P. (2015). Minimizing data redundancy for high reliable cloud storage systems. Computer Networks, 81, 164–177. https://doi.org/10.1016/j.comnet.2015.02.013
There are 26 citations in total.

Details

Primary Language English
Subjects Electrical Engineering (Other)
Journal Section Research Article
Authors

Mahmut Aykaç 0000-0003-2977-9719

Submission Date September 8, 2025
Acceptance Date November 19, 2025
Early Pub Date December 9, 2025
Publication Date January 15, 2026
DOI https://doi.org/10.34248/bsengineering.1780039
IZ https://izlik.org/JA64BJ53GB
Published in Issue Year 2026 Volume: 9 Issue: 1

Cite

APA Aykaç, M. (2026). Layered Encoding With Galois Fourier Transform For Burst Erasure Recovery In Distributed Cloud Storage Systems. Black Sea Journal of Engineering and Science, 9(1), 147-157. https://doi.org/10.34248/bsengineering.1780039
AMA 1.Aykaç M. Layered Encoding With Galois Fourier Transform For Burst Erasure Recovery In Distributed Cloud Storage Systems. BSJ Eng. Sci. 2026;9(1):147-157. doi:10.34248/bsengineering.1780039
Chicago Aykaç, Mahmut. 2026. “Layered Encoding With Galois Fourier Transform For Burst Erasure Recovery In Distributed Cloud Storage Systems”. Black Sea Journal of Engineering and Science 9 (1): 147-57. https://doi.org/10.34248/bsengineering.1780039.
EndNote Aykaç M (January 1, 2026) Layered Encoding With Galois Fourier Transform For Burst Erasure Recovery In Distributed Cloud Storage Systems. Black Sea Journal of Engineering and Science 9 1 147–157.
IEEE [1]M. Aykaç, “Layered Encoding With Galois Fourier Transform For Burst Erasure Recovery In Distributed Cloud Storage Systems”, BSJ Eng. Sci., vol. 9, no. 1, pp. 147–157, Jan. 2026, doi: 10.34248/bsengineering.1780039.
ISNAD Aykaç, Mahmut. “Layered Encoding With Galois Fourier Transform For Burst Erasure Recovery In Distributed Cloud Storage Systems”. Black Sea Journal of Engineering and Science 9/1 (January 1, 2026): 147-157. https://doi.org/10.34248/bsengineering.1780039.
JAMA 1.Aykaç M. Layered Encoding With Galois Fourier Transform For Burst Erasure Recovery In Distributed Cloud Storage Systems. BSJ Eng. Sci. 2026;9:147–157.
MLA Aykaç, Mahmut. “Layered Encoding With Galois Fourier Transform For Burst Erasure Recovery In Distributed Cloud Storage Systems”. Black Sea Journal of Engineering and Science, vol. 9, no. 1, Jan. 2026, pp. 147-5, doi:10.34248/bsengineering.1780039.
Vancouver 1.Mahmut Aykaç. Layered Encoding With Galois Fourier Transform For Burst Erasure Recovery In Distributed Cloud Storage Systems. BSJ Eng. Sci. 2026 Jan. 1;9(1):147-5. doi:10.34248/bsengineering.1780039

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