# Blind Recognition of Forward Error Correction Codes Based on a Depth Distribution Algorithm
## 1 Introduction
Despite these considerable advantages, the algorithm lacked a strict mathematical proof. At the same time, this method was also semi-blind and was hard to be used under the condition of full blind recognition. A blind classification scheme of FEC codes is proposed in [17], which can be applied to the erroneous case. This blind classification scheme requires the knowledge of parameters of FEC codes and the classification performance heavily depends on the accuracy of rank criterion. In order to improve the accuracy of rank criterion, a random row permutation of the intercepted matrix is used, but a theoretical analysis of the accuracy of rank criterion according to the number of random row permutations was not yet performed. In [18], a new algorithm for calculating the rank of intercepted matrix is proposed. This algorithm does not need existing parameters and basically realizes blind recognition, but it does not fundamentally get rid of the problem of poor anti-jamming ability of the matrix rank algorithm. In recent years, forward error correction coding based on a convolution neural network recognition algorithm began to rise, the learning ability of powerful neural networks making it possible to automatically extract the feature identification number type [19; 20]; however, this algorithm needs a large database, and a lot of learning time to ensure the correct recognition algorithm. The practical application prospect also must be observed. Hence a new identification algorithm with a low complexity and a high fault-tolerance is needed, which will be applied to many types of forward error correction codes and is convenient for engineering and practical application. Depth distribution algorithm is a new feature of linear codes first studied by [PERSON] [21] from the perspective of cryptography, and a new method of equivalent linear codes--adeep equivalence class was also proposed at the same time. In [22], the authors proposed a blind parameter estimation of linear block codes based on a depth distribution algorithm based on Etzion. The core algorithm is to obtain the distribution of the depth value through a difference operation and obtain the generation matrix of the depth value under the premise of the code length and code parameters. In this paper, convolutional codes and Turbo codes are equated to linear block codes by code type reconstruction based on traditional algorithms, and a depth distribution algorithm is used to recognize code types. The simulation results show that compared with the traditional matrix rank algorithm, the anti-noise performance of the proposed algorithm is significantly enhanced. In this paper, an improved matrix analysis method based on Gaussian elimination is used to solve the problem of code length and a starting bit of linear block codes under the premise of a perfect frame synchronization of code words. First, use gaussian elimination to the analysis matrix [23; 24], which is based on the symmetry of the matrix, and calculate the normalization of the columns. Then, under the two cases of whether the matrix column vectors are linearly independent, the decision threshold is established according to the different distribution of normalized column weight to find out the location of the maximum number of columns, and determine the length of code based on periodic distribution characteristics. In order to realize the synchronization of the starting bit, the analysis matrix was established under different starting points of the code word, and the corresponding position was found when the number of columns with a low weight was the largest according to the steps of the same length of the code. Therefore, so as to further improve the recognition accuracy, the analysis matrix is randomly exchanged and repeated several times at successive points near the starting point of real code words. Experimental results show that, compared with the traditional Gaussian elimination algorithm, its anti-noise performance is significantly enhanced. The main contributions of this paper are as follows:  
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