## 1 Introduction  
Driven by breakthroughs of deep learning (DL) in image processing, natural language processing and other fields, researchers have proposed channel decoding algorithms based on DL in recent years. DL-based decoding has now become an active area of research. In [1], neural belief propagation (BP) for linear codes was proposed and then the authors applied recurrent neural network (RNN) to linear block codes [2]. Improving decoding performance by adding appropriate weight parameters and loss functions to the decoding algorithm, where the loss function is used to train these weight parameters, is called the model-driven decoding algorithm. The offset min-sum (OMS) decoding algorithm is an excellent decoding method with low complexity and high performance [3], and is widely used in Hamming codes, BCH and low-density parity check (LDPC) codes. However, there is still room for performance improvement in these schemes. [PERSON] and [PERSON] proposed a neural offset min-sum (NOMS) decoding algorithm in 2017. The authors in [4] proposed the model-driven deep learning neural OMS decoding algorithm for LDPC code, and proposed the neural share offset min-sum (NSOMS) decoding algorithm with lower complexity. In [5; 6; 7], both multiplicative weights and offset weights are used in neural scale min-sim (NMS), which needs more storage space and computational complexity. The model-driven BP decoding algorithm achieves state-of-the-art performance and outperforms traditional BP decoder algorithm by adding weights at appropriate locations, which also causes an increase in storage space and computational complexity. However, model-driven BP makes practical implementation challenging. These issues can be solved by model compression techniques. Low rank decomposition is one such model compression technique. Fully connected deep neural network (DNN) parameters are converted into tensor train format through tensor train (TT) decomposition [8]. In [9], it achieves seven times the compression while obtaining a state-of-the-art performance, which converts the fully connected layer to the tensorizing layer. In [10; 11; 12; 13], they converted the dense weight matrices of the fully connected layers and convolutional layers to the tensorizing layer. Recurrent layers in [14; 15] are converted to TT-Recurrent layers. Since tensor decomposition is highly dependent on rank, it is difficult to find the optimal rank that minimizes the error of the product of the decomposed tensors and the original tensor. However, the restricted setting of ranks and restricted ordering of core tensors make TT-based compression models sensitive to parameter selection. The authors of [16] proposed tensor ring (TR) decomposition, which satisfies the circular dimensional permutation invariance. The authors of [17] proposed a TR-based long short-term memory (TR-LSTM) model to reconstruct the input-to-hidden transformation by exploiting tensor ring decomposition, which achieved higher accuracy and higher compression rate than the TT-based long short-term memory (TT-LSTM). TR networks are proposed in [18]. The authors of [19] proposed nonlinear tensor ring networks (NTRN) to compress fully linked neural networks and convolutional neural networks (CNN), which adds a nonlinear activation function after the convolution operation inside the compression layer. TT-based neural normalized min-sum (TT-NNMS) was proposed in [20], which reduces the number of parameters and multiplications. However, ref. [20] only performed TT decomposition for the NNMS decoding algorithm, and did not perform TT decomposition for NOMS. The NOMS algorithm is different from the NNMS algorithm, and the offset addition replaces the factor multiplication in the neural normalized min-sum (NNMS) algorithm. In addition, ref. [20] only applied TT decomposition to the decoding algorithm of LDPC codes, and does not apply it to BCH and Hamming codes.