Advances in Error-Correcting Codes for Emerging Applications

The field of error-correcting codes is witnessing significant developments, driven by emerging applications such as DNA storage and high-rate regimes. Researchers are exploring new code constructions, decoding algorithms, and theoretical bounds to improve the efficiency and reliability of data transmission. Notably, advancements in linear codes for insertion-deletion errors and near-maximum distance separable (NMDS) codes are enhancing the capabilities of error-correcting codes. Furthermore, innovative decoding architectures, such as hybrid normalized min-sum decoders and parallel guessing random additive noise decoders, are being proposed to achieve near-maximum likelihood performance while maintaining advantages in throughput, latency, and complexity. Some noteworthy papers in this area include: Capacity-Achieving Codes for Noisy Insertion Channels, which determines the coding capacity of a new noisy insertion channel and constructs asymptotically optimal error-correcting codes. Improved Constructions of Linear Codes for Insertions and Deletions, which improves upon previous results by constructing explicit codes with rates close to the half-Singleton bound. Neural-Model-Augmented Hybrid NMS-OSD Decoders for Near-ML in Short Block Codes, which introduces a hybrid decoding architecture that achieves near-maximum likelihood performance for short linear block codes.

Sources

Dual and Covering Radii of Extended Algebraic Geometry Codes

Capacity-Achieving Codes for Noisy Insertion Channels

On the Error Rate of Binary BCH Codes under Error-and-erasure Decoding

Neural-Model-Augmented Hybrid NMS-OSD Decoders for Near-ML in Short Block Codes

On the equivalence of NMDS codes

Improved Constructions of Linear Codes for Insertions and Deletions

Coding for Ordered Composite DNA Sequences

Layered Normalized Min-Sum Decoding with Bit Flipping for FDPC Codes

On Algebraic Approaches for DNA Codes with Multiple Constraints

List decoding of evaluation codes

Parallelism Empowered Guessing Random Additive Noise Decoding

The dimension and Bose distance of some BCH codes of length $\frac{q^{m}-1}{\lambda}$

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