We show how techniques from the theory of error-correcting codes can be applied to achieve scalability and hence improved performance. As an exemplar, we focus on how polar codes can be used to efficiently simulate i.i.d.

We show how techniques from the theory of error-correcting codes can be applied to achieve scalability and hence improved performance. As an exemplar, we focus on how polar codes can be used to efficiently simulate i.i.d.

Abstract--In this paper, we adapt and analyze Neural Polar Decoders (NPDs) for end-to-end communication systems. While prior work demonstrated the effectiveness of NPDs on synthetic channels, this study extends the NPD to real-world communication systems. The NPD was adapted to complete OFDM and single-carrier communication systems. T o satisfy practical system requirements, the NPD is extended to support any code length via rate matching, higher-order modulations, and robustness across diverse channel conditions. The NPD operates directly on channels with memory, exploiting their structure to achieve higher data rates without requiring pilots and a cyclic prefix. Although NPD entails higher computational complexity than the standard 5G polar decoder, its neural network architecture enables an efficient representation of channel statistics, resulting in manageable complexity suitable for practical systems. Experimental results over 5G channels demonstrate that the NPD consistently outperforms the 5G polar decoder in terms of BER, BLER, and throughput. These improvements are particularly significant for low-rate and short-block configurations, which are prevalent in 5G control channels. Furthermore, NPDs applied to single-carrier systems offer performance comparable to OFDM with lower PAPR, enabling effective single-carrier transmission over 5G channels. Polar codes, introduced by Arıkan in 2009 [1], are the first class of codes proven to achieve the capacity of symmetric binary-input discrete memoryless channels (B-DMCs) under low-complexity successive cancellation (SC) decoding. In 5G, polar codes are primarily used for control channels, where high performance is required with a low rate and short code length. Their inclusion in the 5G New Radio (NR) standard for uplink and downlink control information, use cases such as enhanced mobile broadband (eMBB) and broadcast channel (BCH) highlight their practical relevance in modern wireless communication systems.

In all cases, the training exploded, similar to the no-threshold vanilla arctanh (l.209,214-215). However in our case, in many of the units, the value explodes at infinity. In the paper (l.203), we ran BP experiments until Running without the absolute value is part of the ablation. Please see the ablation analysis (l.205-216) and note that: (i) hypernetworks allow us to adapt Arikan, "Polar codes: A pipelined implementation"), which makes use of the structure of polar GallagerB, MSA, SP A), while we learn the node activations from scratch. In both codes, our performance is better across all SNR. SNR=5.5 and SNR=6, we obtain a third of their bit error rate (

This paper proposes a method to optimize communication code rates via the application of neural polar decoders (NPDs). Employing this approach enables simultaneous optimization of code rates over input distributions while providing a practical coding scheme within the framework of polar codes. The proposed approach is designed for scenarios where the channel model is unknown, treating the channel as a black box that produces output samples from input samples. We employ polar codes to achieve our objectives, using NPDs to estimate mutual information (MI) between the channel inputs and outputs, and optimize a parametric model of the input distribution. The methodology involves a two-phase process: a training phase and an inference phase. In the training phase, two steps are repeated interchangeably. First, the estimation step estimates the MI of the channel inputs and outputs via NPDs. Second, the improvement step optimizes the input distribution parameters to maximize the MI estimate obtained by the NPDs. In the inference phase, the optimized model is used to construct polar codes. This involves incorporating the Honda-Yamamoto (HY) scheme to accommodate the optimized input distributions and list decoding to enhance decoding performance. Experimental results on memoryless and finite-state channels (FSCs) demonstrate the effectiveness of our approach, particularly in cases where the channel's capacity-achieving input distribution is non-uniform. For these cases, we show significant improvements in MI and bit error rates (BERs) over those achieved by uniform and independent and identically distributed (i.i.d.) input distributions, validating our method for block lengths up to 1024. This scalable approach has potential applications in real-world communication systems, bridging theoretical capacity estimation and practical coding performance.

Polar codes, developed on the foundation of Arikan's polarization kernel, represent a breakthrough in coding theory and have emerged as the state-of-the-art error-correction-code in short-to-medium block length regimes. Importantly, recent research has indicated that the reliability of polar codes can be further enhanced by substituting Arikan's kernel with a larger one, leading to a faster polarization. However, for short-to-medium block length regimes, the development of polar codes that effectively employ large kernel sizes has not yet been realized. In this paper, we explore a novel, non-linear generalization of polar codes with an expanded kernel size, which we call DeepPolar codes. Our results show that DeepPolar codes effectively utilize the benefits of larger kernel size, resulting in enhanced reliability compared to both the existing neural codes and conventional polar codes.

Tailoring polar code construction for decoding algorithms beyond successive cancellation has remained a topic of significant interest in the field. However, despite the inherent nested structure of polar codes, the use of sequence models in polar code construction is understudied. In this work, we propose using a sequence modeling framework to iteratively construct a polar code for any given length and rate under various channel conditions. Simulations show that polar codes designed via sequential modeling using transformers outperform both 5G-NR sequence and Density Evolution based approaches for both AWGN and Rayleigh fading channels.

This paper introduces a novel approach called "friendly attack" aimed at enhancing the performance of error correction channel codes. Inspired by the concept of adversarial attacks, our method leverages the idea of introducing slight perturbations to the neural network input, resulting in a substantial impact on the network's performance. By introducing small perturbations to fixed-point modulated codewords before transmission, we effectively improve the decoder's performance without violating the input power constraint. The perturbation design is accomplished by a modified iterative fast gradient method. This study investigates various decoder architectures suitable for computing gradients to obtain the desired perturbations. Specifically, we consider belief propagation (BP) for LDPC codes; the error correcting code transformer, BP and neural BP (NBP) for polar codes, and neural BCJR for convolutional codes. We demonstrate that the proposed friendly attack method can improve the reliability across different channels, modulations, codes, and decoders. This method allows us to increase the reliability of communication with a legacy receiver by simply modifying the transmitted codeword appropriately.

In communication and storage systems, error correction codes (ECCs) are pivotal in ensuring data reliability. As deep learning's applicability has broadened across diverse domains, there is a growing research focus on neural network-based decoders that outperform traditional decoding algorithms. Among these neural decoders, Error Correction Code Transformer (ECCT) has achieved the state-of-the-art performance, outperforming other methods by large margins. To further enhance the performance of ECCT, we propose two novel methods. First, leveraging the systematic encoding technique of ECCs, we introduce a new masking matrix for ECCT, aiming to improve the performance and reduce the computational complexity. Second, we propose a novel transformer architecture of ECCT called a double-masked ECCT. This architecture employs two different mask matrices in a parallel manner to learn more diverse features of the relationship between codeword bits in the masked self-attention blocks. Extensive simulation results show that the proposed double-masked ECCT outperforms the conventional ECCT, achieving the state-of-the-art decoding performance with significant margins.