Deep Learning-Based Bit Reliability Based Decoding for Non-binary LDPC Codes

Watanabe, Taishi; Ohseki, Takeo; Yamazaki, Kosuke

doi:10.1109/isit45174.2021.9517790

Cited by 5 publications

(9 citation statements)

References 15 publications

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“…In this paper, we follow the second interpretation for maximizing the margin induced by the channel decoder. This approach leads to an RLM problem with the hinge loss over the transformed noise samples and a codebook related regularization in (10). Hence, unlike SVM, the two approaches lead to different optimization problems for the channel decoding problem, where the main source of difference is in fact due to the lower bound taken in step 2.…”

Section: A the Additive Noise Channel Rlmmentioning

confidence: 99%

“…In this section, we state average generalization error bounds on the expected error probability, for the RLM learning rules (10) and (19). Additionally, we show an optimal choice for λ, the regularization parameter.…”

Section: Generalization Error Boundsmentioning

confidence: 99%

“…Theorem 5. Let A be the RLM rule (10), and let µ be the distribution of the noise Z. If r x max x∈C x , η min min i∈[d+1] {η i }, the noise Z is sub-Gaussian with variance proxy σ 2 Z , and…”

Section: Generalization Error Boundsmentioning

confidence: 99%

“…Next, we apply [21,Cor. 13.6], where we replace the 2-strong-convexity of the Tikhonov regularization with the appropriate constant for the regularization function of (10). Then, we get from [21,Cor.…”

Section: Generalization Error Boundsmentioning

confidence: 99%

“…The success of machine learning (ML) based methods in various domains have spurred a great contemporary interest in the application of ML algorithms to communication problems [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. However, state-of-the art communication systems heavily rely on expert-based design, and so obtaining a significantly improved performance with ML algorithms typically necessitates the use of the most advanced ML algorithms, most notably, deep neural networks (DNN).…”

Section: Introductionmentioning

confidence: 99%

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Learning Maximum Margin Channel Decoders

Tsvieli¹,

Weinberger²

2022

Preprint

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The problem of learning a channel decoder is considered for two channel models. The first model is an additive noise channel whose noise distribution is unknown and nonparametric. The learner is provided with a fixed codebook and a dataset comprised of independent samples of the noise, and is required to select a precision matrix for a nearest neighbor decoder in terms of the Mahalanobis distance. The second model is a non-linear channel with additive white Gaussian noise and unknown channel transformation. The learner is provided with a fixed codebook and a dataset comprised of independent input-output samples of the channel, and is required to select a matrix for a nearest neighbor decoder with a linear kernel. For both models, the objective of maximizing the margin of the decoder is addressed. Accordingly, for each channel model, a regularized loss minimization problem with a codebook-related regularization term and hinge-like loss function is developed, which is inspired by the support vector machine paradigm for classification problems. Expected generalization error bounds for the error probability loss function are provided for both models, under optimal choice of the regularization parameter. For the additive noise channel, a theoretical guidance for choosing the training signal-to-noise ratio is proposed based on this bound. In addition, for the non-linear channel, a high probability uniform generalization error bound is provided for the hypothesis class.For each channel, a stochastic sub-gradient descent algorithm for solving the regularized loss minimization problem is proposed, and an optimization error bound is stated. The performance of the proposed algorithms is demonstrated through several examples.

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Section: A the Additive Noise Channel Rlmmentioning

confidence: 99%

Section: Generalization Error Boundsmentioning

confidence: 99%

Section: Generalization Error Boundsmentioning

confidence: 99%

Section: Generalization Error Boundsmentioning

confidence: 99%