Transformer-based neural decoders have emerged as a promising approach to error correction coding, combining data-driven adaptability with efficient modeling of long-range dependencies. This paper presents a novel decoder architecture that integrates classical belief propagation principles with transformer designs. We introduce a differentiable syndrome loss function leveraging global codebook structure and a differential-attention mechanism optimizing bit and syndrome embedding interactions. Experimental results demonstrate consistent performance improvements over existing transformer-based decoders, with our approach surpassing traditional belief propagation decoders for short-to-medium length LDPC codes.

We consider sparse regression codes (SPARCs) for the multiple-input multiple-output (MIMO) detection problem. Specifically, we introduce normals with unknown variances (NUV) priors to represent one-hot vectors in SPARCs and derive the corresponding NUV-EM algorithm accordingly. Then, we apply this algorithm to MIMO detection problems. In order to tackle issues arising from the proposed NUV-EM algorithm, a (Hadamard-based) Gaussian generalized approximate message passing (GAMP) algorithm, along with a simple rejection technique, is proposed. Simulation results show that our proposed algorithms work well over various channels.

We consider sparse regression codes (SPARCs) over complex AWGN channels. Such codes can be efficiently decoded by an approximate message passing (AMP) decoder, whose performance can be predicted via so-called state evolution in the large-system limit. In this paper, we mainly focus on how to use concatenation of SPARCs and cyclic redundancy check (CRC) codes on the encoding side and use list decoding on the decoding side to improve the finite-length performance of the AMP decoder for SPARCs over complex AWGN channels. Simulation results show that such a concatenated coding scheme works much better than SPARCs with the original AMP decoder and results in a steep waterfall-like behavior in the bit-error rate performance curves. Furthermore, we apply our proposed concatenated coding scheme to spatially coupled SPARCs. Besides that, we also introduce a novel class of design matrices, i.e., matrices that describe the encoding process, based on circulant matrices derived from Frank or from Milewski sequences. This class of design matrices has comparable encoding and decoding computational complexity as well as very close performance with the commonly-used class of design matrices based on discrete Fourier transform (DFT) matrices, but gives us more degrees of freedom when designing SPARCs for various applications.

We consider sparse superposition codes (SPARCs) over complex AWGN channels. Such codes can be efficiently decoded by an approximate message passing (AMP) decoder, whose performance can be predicted via so-called state evolution in the large-system limit. In this paper, we mainly focus on how to use concatenation of SPARCs and cyclic redundancy check (CRC) codes on the encoding side and use list decoding on the decoding side to improve the finite-length performance of the AMP decoder for SPARCs over complex AWGN channels. Simulation results show that such a concatenated coding scheme works much better than SPARCs with the original AMP decoder and results in a steep waterfall-like behavior in the bit-error rate performance curves.

Erasure codes provide higher reliability than replication for a same level of redundancy to store data in distributed storage systems, yet with more bandwidth overhead. Recently, regenerating codes are introduced, which significantly reduce the repair bandwidth by analyzing the fundamental tradeoff between storage capacity and repair bandwidth via the information flow graph. In reality, distributed storage systems with hierarchical structures are more common in data centers where data are organized in racks, and the cross-rack communication is more costly than the in-rack communication. Hence, in this paper, we introduce a class of codes to repair a failed node by downloading data from nodes in the same rack only, which are termed as multi-rack regenerating codes (MRC). Different with existing works, the cross-rack repair bandwidth under our codes can be reduced to zero. Meanwhile, we obtain the optimal tradeoff between storage and bandwidth of MRC, and present an explicit construction of MRC with the common product-matrix framework.