Autoencoder-Based Error Correction Coding for One-Bit Quantization

Abstract

This paper proposes a novel deep learning-based error correction coding scheme for AWGN channels under the constraint of one-bit quantization in the receivers. Specifically, it is first shown that the optimum error correction code that minimizes the probability of bit error can be obtained by perfectly training a special autoencoder, in which "perfectly" refers to converging the global minima. However, perfect training is not possible in most cases.To approach the performance of a perfectly trained autoencoder with a suboptimum training, we propose utilizing turbo codes as an implicit regularization, i.e., using a concatenation of a turbo code and an autoencoder. It is empirically shown that this design gives nearly the same performance as to the hypothetically perfectly trained autoencoder, and we also provide a theoretical proof of why that is so. The proposed coding method is as bandwidth efficient as the integrated (outer) turbo code, since the autoencoder exploits the excess bandwidth from pulse shaping and packs signals more intelligently thanks to sparsity in neural networks. Our results show that the proposed coding scheme at finite block lengths outperforms conventional turbo codes even for QPSK modulation. Furthermore, the proposed coding method can make one-bit quantization operational even for 16-QAM.

Deep Learning-Assisted TeraHertz QPSK Detection Relying on Single-Bit Quantization

“…For example, Balevi and Andrews [22] developed a novel deep learning based single-bit receiver for orthogonal frequency division multiplexing (OFDM), where generative supervised deep neural networks and unsupervised autoencoder detection methods are utilized for estimating the channel and detecting the signal, respectively. Balevi and Andrews [23] also transformed the design of hand-crafted channel codes into the learning of a specially designed autoencoder relying on single-bit quantization. Jeon et al [24] utilized reinforcement learning, while Zhang et al [25] used deep learning, respectively, for signal detection and for channel estimation in multiple-input multiple-output (MIMO) systems.…”

Residual-Aided End-to-End Learning of Communication System without Known Channel

“…This is caused by the fact that the regularizer will limit the representation ability of the E2E learning of communication system. If we decrease the hyper-parameter λ in (10), the optimal BLER performance will be achieved, but the BLER performance will degrade in low E b /N 0 regions.…”

“…In contrast to the classical signal processing algorithms, which are usually complex in wireless communication systems [4], deep learning based E2E learning can realize the modulation and other functions by simple addition and multiplication operations between each layer of the DNN. Thus, the E2E learning of communication system could reach or even outperform the conventional system with lower complexity [1], [5]- [10].…”

“…Generate N train training data samples at random; Initialize weights θ D , θ G , θ R , and θ T according to the Xavier initialization method [25]; 4 for epoch = 1, 2, • • •, Epoch do 5 for index = 1, 2, • • •, Index do B one-hot vectors as training samples; Caculate transmitted signals: x (1) , • • •, x (B) ; B channel samples: h (1) , • • •, h (B) ; Get real received signals: y (1) , • • •, y (B) ; 10 Generate fake received signals: y (1) , • • •, y (B) ; 11 for i ∈ {D, G, R, T } do 12 Caculate the loss function L (θ i ) according to (10);13Use ∇ θ i L (θ i ) to update θ i according to the Adam method[21]; penalty item Ω (θ i ) in(10) only introduces limited operations when we compute the new loss function and gradient in each iteration. The computational complexity after reconstructing the loss function isO (|θ D | + |θ G | + |θ R | + |θ T |), where |θ| denote the number of weights in θ.…”

High Rate Communication over One-Bit Quantized Channels via Deep Learning and LDPC Codes

“…However, for high order modulations one-bit quantization leads to a very poor error rate, since the real and the imaginary part of the signals carry more than one bit information. The closest paper to this work is [8], which proposed to integrate a turbo code to an autoencoder to handle the detrimental effects of onebit quantization for QPSK and 16-QAM signaling. The main difference of this paper is to (i) use an LDPC code instead of a turbo code; (ii) utilize a modified autoencoder architecture; and (iii) propose a simpler, but efficient training policy that gives us better error rate for high order modulations, e.g., 64-QAM can be operable for one-bit quantization at sufficiently low SNRs.…”