Decoding algebraic block codes is an open problem and learning techniques have recently been introduced to this field.

We show in this work that reinforcement learning can be successfully applied to decoding short to moderate length sparse graph-based channel codes. Specifically, we focus on low-density parity check (LDPC) codes, which for example have been standardized in the context of 5G cellular communication systems due to their excellent error correcting performance. These codes are typically decoded via belief propagation iterative decoding on the corresponding bipartite (Tanner) graph of the code via flooding, i.e., all check and variable nodes in the Tanner graph are updated at once. In contrast, in this paper we utilize a sequential update policy which selects the optimum check node (CN) scheduling in order to improve decoding performance. In particular, we model the CN update process as a multi-armed bandit process with dependent arms and employ a Q-learning scheme for optimizing the CN scheduling policy. In order to reduce the learning complexity, we propose a novel graph-induced CN clustering approach to partition the state space in such a way that dependencies between clusters are minimized. Our results show that compared to other decoding approaches from the literature, the proposed reinforcement learning scheme not only significantly improves the decoding performance, but also reduces the decoding complexity dramatically once the scheduling policy is learned.

Decoding algebraic block codes is an open problem and learning techniques have recently been introduced to this field.

This paper presents a novel auto-encoder based end-to-end channel encoding and decoding. It integrates deep reinforcement learning (DRL) and graph neural networks (GNN) in code design by modeling the generation of code parity-check matrices as a Markov Decision Process (MDP), to optimize key coding performance metrics such as error-rates and code algebraic properties. An edge-weighted GNN (EW-GNN) decoder is proposed, which operates on the Tanner graph with an iterative message-passing structure. Once trained on a single linear block code, the EW-GNN decoder can be directly used to decode other linear block codes of different code lengths and code rates. An iterative joint training of the DRL-based code designer and the EW-GNN decoder is performed to optimize the end-end encoding and decoding process. Simulation results show the proposed auto-encoder significantly surpasses several traditional coding schemes at short block lengths, including low-density parity-check (LDPC) codes with the belief propagation (BP) decoding and the maximum-likelihood decoding (MLD), and BCH with BP decoding, offering superior error-correction capabilities while maintaining low decoding complexity.

Error correction codes (ECC) are crucial for ensuring reliable information transmission in communication systems. Choukroun & Wolf (2022b) recently introduced the Error Correction Code Transformer (ECCT), which has demonstrated promising performance across various transmission channels and families of codes. However, its high computational and memory demands limit its practical applications compared to traditional decoding algorithms. Achieving effective quantization of the ECCT presents significant challenges due to its inherently small architecture, since existing, very low-precision quantization techniques often lead to performance degradation in compact neural networks. In this paper, we introduce a novel acceleration method for transformer-based decoders. We first propose a ternary weight quantization method specifically designed for the ECCT, inducing a decoder with multiplication-free linear layers. We present an optimized self-attention mechanism to reduce computational complexity via codeaware multi-heads processing. Finally, we provide positional encoding via the Tanner graph eigendecomposition, enabling a richer representation of the graph connectivity. The approach not only matches or surpasses ECCT's performance but also significantly reduces energy consumption, memory footprint, and computational complexity. Our method brings transformer-based error correction closer to practical implementation in resource-constrained environments, achieving a 90% compression ratio and reducing arithmetic operation energy consumption by at least 224 times on modern hardware.

The design of optimal linear block codes capable of being efficiently decoded is of major concern, especially for short block lengths. As near capacity-approaching codes, Low-Density Parity-Check (LDPC) codes possess several advantages over other families of codes, the most notable being its efficient decoding via Belief Propagation. While many LDPC code design methods exist, the development of efficient sparse codes that meet the constraints of modern short code lengths and accommodate new channel models remains a challenge. In this work, we propose for the first time a data-driven approach for the design of sparse codes. We develop locally optimal codes with respect to Belief Propagation decoding via the learning on the Factor graph (also called the Tanner graph) under channel noise simulations. This is performed via a novel tensor representation of the Belief Propagation algorithm, optimized over finite fields via backpropagation coupled with an efficient line-search method. The proposed approach is shown to outperform the decoding performance of existing popular codes by orders of magnitude and demonstrates the power of data-driven approaches for code design.

Error correction codes are a crucial part of the physical communication layer, ensuring the reliable transfer of data over noisy channels. The design of optimal linear block codes capable of being efficiently decoded is of major concern, especially for short block lengths. While neural decoders have recently demonstrated their advantage over classical decoding techniques, the neural design of the codes remains a challenge. In this work, we propose for the first time a unified encoder-decoder training of binary linear block codes. To this end, we adapt the coding setting to support efficient and differentiable training of the code for end-to-end optimization over the order two Galois field. We also propose a novel Transformer model in which the self-attention masking is performed in a differentiable fashion for the efficient backpropagation of the code gradient. Our results show that (i) the proposed decoder outperforms existing neural decoding on conventional codes, (ii) the suggested framework generates codes that outperform the {analogous} conventional codes, and (iii) the codes we developed not only excel with our decoder but also show enhanced performance with traditional decoding techniques.

In decoding linear block codes, it was shown that noticeable reliability gains can be achieved by introducing learnable parameters to the Belief Propagation (BP) decoder. Despite the success of these methods, there are two key open problems. The first is the lack of interpretation of the learned weights, and the other is the lack of analysis for non-AWGN channels. In this work, we aim to bridge this gap by providing insights into the weights learned and their connection to the structure of the underlying code. We show that the weights are heavily influenced by the distribution of short cycles in the code. We next look at the performance of these decoders in non-AWGN channels, both synthetic and over-the-air channels, and study the complexity vs. performance trade-offs, demonstrating that increasing the number of parameters helps significantly in complex channels. Finally, we show that the decoders with learned weights achieve higher reliability than those with weights optimized analytically under the Gaussian approximation.

In this work, we propose a novel decoding algorithm for short block codes based on an edge-weighted graph neural network (EW-GNN). The EW-GNN decoder operates on the Tanner graph with an iterative message-passing structure, which algorithmically aligns with the conventional belief propagation (BP) decoding method. In each iteration, the "weight" on the message passed along each edge is obtained from a fully connected neural network that has the reliability information from nodes/edges as its input. Compared to existing deep-learning-based decoding schemes, the EW-GNN decoder is characterised by its scalability, meaning that 1) the number of trainable parameters is independent of the codeword length, and 2) an EW-GNN decoder trained with shorter/simple codes can be directly used for longer/sophisticated codes of different code rates. Furthermore, simulation results show that the EW-GNN decoder outperforms the BP and deep-learning-based BP methods from the literature in terms of the decoding error rate.