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.

A novel single parity check-multiplicity assignment decoding algorithm based on voltage magnitude (VM_SPC-MA) is proposed, which is applied to the concatenated scheme of single parity check (SPC) inner code and Reed-Solomon (RS) outer code, following the Consultative Committee for Space Data Systems (CCSDS) standard. The algorithm determines whether the SPC code is in error by SPC, then obtains the reliability information of the inner code bits for error correction based on the characteristics of the received bit-level voltage, and decodes the outer code based on the reliability information of the inner codewords and the channel information. The decoding performance is greatly improved by connecting the inner and outer codes through the multiplicity assignment (MA) module, which makes full use of the channel information. Compared with the low-complexity Chase decoding based on the hard-decision decoding (HDD-LCC) and SPC_Kaneko-RS_Chase decoding, simulation results show that the SPC-RS concatenated decoding scheme based on VM_SPC-MA algorithm can provide up to 1.78 and 1.05 dB of coding gain when the bit error rate is (BER) = 10 ^-5 . Besides, the hardware design of the SPC-MA module is provided and applied to the serial LCC decoder based on syndrome calculation-polynomial selection (PS)-Chien search and Forney algorithm (SPCF). The implementation results in ASIC show that the area efficiency of the complete concatenated decoder increases by 27.38% compared to the unified syndrome computation (USC)-based LCC decoder in a 0.13- μm process.

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 .

In non-cooperative communication systems, the effective recognition by intercepted bitstream at the 3rd-party receiver is an important mission for military or security purposes. However, the existing recognition schemes lead to long latency and significant hardware due to the large number of traversal operations. Hence, the spectra update algorithm (SUA) is proposed by analyzing the differences between the adjacent reconstructed matrices. Compared with the spectra calculations available like the Galois field Fourier transform (GFFT) and simplified-GFFT (S-GFFT), the presented algorithm reduces the computational complexity to 2/ n and 2/λ without performance loss, respectively, where n is the code length and λ is the cardinality of the conjugacy class of the corresponding Galois fields. Besides, a reduced-complexity RS recognizer architecture is designed and analyzed to show the effectiveness of the proposed SUA.