• KSII Transactions on Internet and Information Systems
    Monthly Online Journal (eISSN: 1976-7277)

A Two-Step Screening Algorithm to Solve Linear Error Equations for Blind Identification of Block Codes Based on Binary Galois Field


Abstract

Existing methods for blind identification of linear block codes without a candidate set are mainly built on the Gauss elimination process. However, the fault tolerance will fall short when the intercepted bit error rate (BER) is too high. To address this issue, we apply the reverse algebra approach and propose a novel “two-step-screening” algorithm by solving the linear error equations on the binary Galois field, or GF(2). In the first step, a recursive matrix partition is implemented to solve the system linear error equations where the coefficient matrix is constructed by the full codewords which come from the intercepted noisy bitstream. This process is repeated to derive all those possible parity-checks. In the second step, a check matrix constructed by the intercepted codewords is applied to find the correct parity-checks out of all possible parity-checks solutions. This novel “two-step-screening” algorithm can be used in different codes like Hamming codes, BCH codes, LDPC codes, and quasi-cyclic LDPC codes. The simulation results have shown that it can highly improve the fault tolerance ability compared to the existing Gauss elimination process-based algorithms.


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Cite this article

[IEEE Style]
Q. Liu, H. Zhang, P. Yu, G. Wang and Z. Qiu, "A Two-Step Screening Algorithm to Solve Linear Error Equations for Blind Identification of Block Codes Based on Binary Galois Field," KSII Transactions on Internet and Information Systems, vol. 15, no. 9, pp. 3458-3481, 2021. DOI: 10.3837/tiis.2021.09.020.

[ACM Style]
Qian Liu, Hao Zhang, Peidong Yu, Gang Wang, and Zhaoyang Qiu. 2021. A Two-Step Screening Algorithm to Solve Linear Error Equations for Blind Identification of Block Codes Based on Binary Galois Field. KSII Transactions on Internet and Information Systems, 15, 9, (2021), 3458-3481. DOI: 10.3837/tiis.2021.09.020.

[BibTeX Style]
@article{tiis:24943, title="A Two-Step Screening Algorithm to Solve Linear Error Equations for Blind Identification of Block Codes Based on Binary Galois Field", author="Qian Liu and Hao Zhang and Peidong Yu and Gang Wang and Zhaoyang Qiu and ", journal="KSII Transactions on Internet and Information Systems", DOI={10.3837/tiis.2021.09.020}, volume={15}, number={9}, year="2021", month={September}, pages={3458-3481}}