This letter presents a fast blind recognition method for Bose, Chaudhuri, and Hocquenghem (BCH) code from noisy intercepted bit-streams. This approach employs the fact that the t-error-correcting BCH code has 2t continuous roots, and the roots correspond with the zero spectral. Specifically, the Galois field Fourier transform is simplified (S-GFFT) by using the property of conjugate roots. Then, the distribution characteristics of continuous zero spectra are analyzed. If the continuous zero spectra satisfy the threshold condition which is derived by the probability of zero spectrum component, the corresponding estimated length is the code length, and the relevant positions correspond to the continuous roots of the generated polynomial. Finally, the generator polynomial can be reconstructed based on algebras theory. Compared to the existing solutions, the computational amount of S-GFFT at most accounts for 60% of GFFT, and the proposed scheme manages to recognize the code parameters without traversing the whole candidate datasets.

In non-cooperative communication systems, effective parameter identification with small samples intercepted bitstream is a major challenge. Faced with this demand, a solution to blind recognition for BCH and RS codes is presented. Firstly, the intercepted bitstream is analyzed, and the optimal code-set with high reliability is selected by channel soft information. Secondly, the optimal code-set is cycled into a pseudo cyclic matrix according to the algebraic structure of the codewords, which is employed for the code length and synchronization recognition based on the improved rank criterion. Finally, the code spectrum analysis of the optimal code-set is performed to complete primitive and generator polynomial recognition, and a recoding operation is proposed to judge the recognition performance. Simulations validate the proposed algorithms by recognition probability in terms of different parameters, it hardly depends on the number of codewords but on the accuracy of the optimal code-set, which is especially suitable for small sample datasets. Under the Additive White Gaussian Noise (AWGN) channel with Binary Phase-Shift Keying (BPSK) modulation, the recognition probability is still comparable to or superior to the existing schemes, even if only one-twentieth of the intercepted codewords are used.

Visible light communication (VLC) offers a unique advantage of electromagnetic interference immunity and wide bandwidth. It has gradually become the main candidate in marine communication with great potential. As a green communication link, VLC requires reliable beam tracking as a prerequisite. Therefore, based on the received signal strength of a single-input–multiple-output system in the VLC scenario, this paper first proposes a geometrical algorithm for transmitter localization. On this basis, a linear iterative algorithm using Taylor expansion, implicit function theorem, and time-domain expansion is presented to realize online beam tracking. Under the marine VLC system, an iterative denoising algorithm based on the hidden Markov model and principal component analysis is proposed for denoising. Simulation results show that the proposed algorithms have predominance in high tracking accuracy (within 10 cm) and desirable real-time performance.

The Galois field Fourier transform (GFFT) method has been widely applied in the blind recognition of Reed-Solomon (RS) codes in recent years. However, as the code length increases, the computational complexity increases rapidly. Also, blind recognition in a poor channel environment remains challenging. To solve the above challenges, a blind recognition algorithm is proposed based on GFFT and reliability verification (RV). Low-complexity GFFT (LC-GFFT) is proposed to calculate the shortened spectrums, reducing the computational complexity and improving the correct codeword utilization rate (CUR). Next, the criteria for parameter estimation (PE) are given. The RV module is designed to verify the correctness of the estimated parameters. The simulations demonstrate that our algorithm can recognize RS(15, 11, 2, 19) and RS(31, 15, 8, 37) with over 95% correct rate when SNR is above 0.8dB and 2.5dB, achieving at least 7dB of signal-to-noise (SNR) defined gain over the existing algorithms. Moreover, the recognition time of our method is reduced by 74.8% compared to that of the GFFT-based method for RS(31, 15, 8, 37) when N = 1 × 10 ⁵ .

In this letter, two novel single parity-check aided (SPC-aided) adaptive belief propagation (ABP) decoding algorithms are proposed for Reed-Solomon (RS) codes. SPC codes can be used to evaluate the reliability of the information bits in the received RS codewords and modify the log-likelihood ratio (LLR) values of the probably incorrect bits, which can greatly reduce the influence of the pseudo-equilibrium points on the traditional ABP algorithm. Based on this idea, we propose an SPC-aided ABP decoding algorithm. In addition, a new selection scheme of unreliable bits to be sparsified is proposed with the aid of SPC codes. Combining the SPC-aided ABP and this new selection scheme, an enhanced SPC-aided (E-SPC-aided) ABP algorithm is further proposed. The complexity and latency analysis results demonstrate that the two proposed algorithms have lower complexity and decoding latency than the dynamic scheduling strategies. Compared with the traditional ABP, LRBP and HD-P-ABP, simulation results show that the E-SPC-aided ABP algorithm can provide error-correction performance gains of up to 1.1 dB, 0.7 dB and 0.5 dB for RS(255,239) code, respectively at the FER = 10 ⁻³ .