Density Estimation of Processes with Memory via Donsker Vardhan

Aharoni, Ziv; Tsur, Dor; Permuter, Haim H.

doi:10.1109/isit50566.2022.9834775

Cited by 2 publications

(2 citation statements)

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“…The first trains the embedding and the NSC jointly. The second determines the parameters of the embedding E using neural estimation methods [7]- [9], and then, determines the parameters of the NSC while the parameters of E are fixed. After the training phase, the set of "clean" effective channels are determined by a Monte Carlo (MC) evaluation of the MI of the effective bit channels to complete the code design.…”

Section: A Contributionmentioning

confidence: 99%

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Data-Driven Polar Codes for Unknown Channels With and Without Memory

Aharoni,

Huleihel,

Pfister

et al. 2023

2023 IEEE International Symposium on Information Theory (ISIT)

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In this work, a novel data-driven methodology for designing polar codes for channels with and without memory is proposed. The methodology is suitable for the case where the channel is given as a "black-box" and the designer has access to the channel for generating observations of its inputs and outputs, but does not have access to the explicit channel model. The proposed method leverages the structure of the successive cancellation (SC) decoder to devise a neural SC (NSC) decoder. The NSC decoder uses neural networks (NNs) to replace the core elements of the original SC decoder, the check-node, the bit-node and the soft decision. Along with the NSC, we devise additional NN that embeds the channel outputs into the input space of the SC decoder. The proposed method is supported by theoretical guarantees that include the consistency of the NSC. Also, the NSC has computational complexity that does not grow with the channel memory size. This sets its main advantage over successive cancellation trellis (SCT) decoder for finite state channels (FSCs) that has complexity of O(|S| 3 N log N ), where |S| denotes the number of channel states. We demonstrate the performance of the proposed algorithms on memoryless channels and on channels with memory. The empirical results are compared with the optimal polar decoder, given by the SC and SCT decoders. We further show that our algorithms are applicable for the case where there SC and SCT decoders are not applicable.

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Section: A Contributionmentioning

confidence: 99%

“…Similar to [25], we choose ǫ 0 = 0.4, ǫ 1 = 0.8159. Bit error rate P X (1) = 9 16 , E W P X (1) = 1 2 , E W Figure 2 shows the application of Algorithm 1 on the BSC and the AWGN channels. It reports the obtained BERs by Algorithm 1 in comparison with the SC decoder.…”

Section: A Memoryless Channelsmentioning

confidence: 99%