Deep learning has shown an unprecedented success in many fields such as computer vision and speech recognition, providing solutions to intractable problems. Deep learning has also provided solutions to several intractable problems in communications systems. This paper uses a deep learning approach to optimize the analytically intractable offset value in the offset-min-sum (OMS) algorithm. OMS algorithm is a very attractive low complexity algorithm that is used in the belief propagation decoding of linear codes. The contributions of this paper are: First, providing a low complexity offset optimization framework based on gradient descent and back propagation on the original Tanner graph. Our proposed algorithm has comparable complexity and similar operation as the forward belief propagation decoding algorithm and hence, can be trained much more efficiently. Second, the framework can be easily extended to any decoding scheduling such as flooding or layered scheduling. Training results show that the proposed framework can find the optimal offset value under different decoding scheduling with the same complexity of the belief propagation algorithm.
Deep learning has shown an unprecedented success in many fields such as computer vision and speech recognition, providing solutions to intractable problems. Deep learning has also provided solutions to several intractable problems in communications systems. This paper uses a deep learning approach to optimize the analytically intractable offset value in the offset-min-sum (OMS) algorithm. OMS algorithm is a very attractive low complexity algorithm that is used in the belief propagation decoding of linear codes. The contributions of this paper are: First, providing a low complexity offset optimization framework based on gradient descent and back propagation on the original Tanner graph. Our proposed algorithm has comparable complexity and similar operation as the forward belief propagation decoding algorithm and hence, can be trained much more efficiently. Second, the framework can be easily extended to any decoding scheduling such as flooding or layered scheduling. Training results show that the proposed framework can find the optimal offset value under different decoding scheduling with the same complexity of the belief propagation algorithm.
In this paper, we propose two novel min-sum (MS) decoding algorithms based on deep learning for polar codes, an offset min-sum (OMS) and a scaling offset min-sum (SOMS) algorithm. The parameters of both algorithms are different from iteration to iteration, and are obtained by training over a deep neural network. Our simulation results show that the OMS algorithm has roughly the same error performance as a previously proposed multiple scaling min-sum (MSMS) algorithm, and that the SOMS algorithm performs better than all existing BP-based algorithms. Since the OMS algorithm requires only an addition as opposed to a multiplication in the MSMS algorithm, the OMS algorithm is more suitable for hardware implementation. The two proposed decoding algorithms provide a tradeoff between complexity and error performance.
This paper presents deep learning (DL) methods to optimize polar belief propagation (BP) decoding and concatenated LDPC-polar codes. First, two-dimensional offset Min-Sum (2-D OMS) decoding is proposed to improve the error-correction performance of existing normalized Min-Sum (NMS) decoding. Two optimization methods used in DL, namely back-propagation and stochastic gradient descent, are exploited to derive the parameters of proposed algorithms. Numerical results demonstrate that there is no performance gap between 2-D OMS and exact BP on various code lengths. Then the concatenated OMS algorithms with low complexity are presented for concatenated LDPC-polar codes. As a result, the optimized concatenated OMS decoding yields error-correction performance with CRC-aided successive cancellation list (CA-SCL) decoder of list size 2 on length-1024 polar codes. In addition, the efficient hardware architectures of scalable polar OMS decoder are described and the proposed decoder is reconfigurable to support three code lengths (N = 256, 512, 1024) and two decoding algorithms (2-D OMS and concatenated OMS). The polar OMS decoder implemented on 65 nm CMOS technology achieves a maximum coded throughput of 5.4 Gb/s at Eb/N0= 4 dB for code length 1024 and 7.5 Gb/s at Eb/N0= 3.5 dB for code length 256, which are comparable to the state-of-the-art polar BP decoders. Moreover, a 5.1 Gb/s throughput at Eb/N0= 4 dB is achieved under concatenated OMS decoding mode for code length 1024 with a latency of 200 ns, which is superior to existing CA-SCL decoders that have similar error-correction performance.
Recently, it was shown that if multiplicative weights are assigned to the edges of a Tanner graph used in belief propagation decoding, it is possible to use deep learning techniques to find values for the weights which improve the error-correction performance of the decoder. Unfortunately, this approach requires many multiplications, which are generally expensive operations. In this paper, we suggest a more hardware-friendly approach in which offset min-sum decoding is augmented with learnable offset parameters. Our method uses no multiplications and has a parameter count less than half that of the multiplicative algorithm. This both speeds up training and provides a feasible path to hardware architectures. After describing our method, we compare the performance of the two neural decoding algorithms and show that our method achieves error-correction performance within 0.1 dB of the multiplicative approach and as much as 1 dB better than traditional belief propagation for the codes under consideration.
The problem of low complexity, close to optimal, channel decoding of linear codes with short to moderate block length is considered. It is shown that deep learning methods can be used to improve a standard belief propagation decoder, despite the large example space. Similar improvements are obtained for the min-sum algorithm. It is also shown that tying the parameters of the decoders across iterations, so as to form a recurrent neural network architecture, can be implemented with comparable results. The advantage is that significantly less parameters are required. We also introduce a recurrent neural decoder architecture based on the method of successive relaxation. Improvements over standard belief propagation are also observed on sparser Tanner graph representations of the codes. Furthermore, we demonstrate that the neural belief propagation decoder can be used to improve the performance, or alternatively reduce the computational complexity, of a close to optimal decoder of short BCH codes.
Deep learning-based decoding algorithms have emerged as a focal point currently in contemporary research. Neural Offset Min-Sum Belief Propagation decoding algorithm is one of the traditional deep learning methods rooted in model-driven approaches. However, with the gradual increase in codeword length, there is an inevitable surge in the training cost and time complexity of such kind of deep learning algorithms. Addressing this issue, a novel deep learning algorithm based on the structural characteristics of the base graph in protograph LDPC codes is proposed. By strategically training the base graph and introducing a unique bit decoding allocation strategy, we endeavor to harmonize the Deep Learning algorithm with the intrinsic structure of the base graph itself. This approach contrasts favorably with several existing methods that utilize conventional segmental deep learning decoding algorithms for protograph LDPC codes. Simulation results demonstrate that, compared to other model-driven based deep learning algorithms, the proposed algorithm significantly reduces the number of parameters required for storage and training, while the loss in decoding performance remains within acceptable bounds.
In recent years, the emerging Deep Learning (DL) technology has made progress in the field of decoding. Current polar code neural network decoder has faster convergence speed and better Bit Error Rate (BER) performance than Belief Propagation (BP) decoding. However, it still has the problem of high computational complexity. Therefore, in order to improve this problem, this paper adopts the idea of improving information update in the iterative process, and proposes a Recurrent Neural Network (RNN) Offset Min-Sum (OMS) BP decoding algorithm that improves Left information update (RNN-OMSBP-L) . The simulation results show that, compared with the Deep Neural Network (DNN) BP(DNN-BP) decoding algorithm, this algorithm replaces all multiplications with a cost of 6.25% addition. Compared with the current optimized RNN OMS and approximate BP(RNN-OMS-BP) decoding algorithm, the decoding algorithm in this paper uses improved information to reduce 25% of the addition operations with almost no loss in BER performance, while saving part of the storage space overhead. Under the same BER performance, it reduces the number of iterations by 37.5%.