Related papers: Biff (Bloom Filter) Codes : Fast Error Correction …
The Bloom filter (BF) is a well-known space-efficient data structure that answers set membership queries with some probability of false positives. In an attempt to solve many of the limitations of current inter-networking architectures,…
Motivated by distributed storage applications, we investigate the degree to which capacity achieving encodings can be efficiently updated when a single information bit changes, and the degree to which such encodings can be efficiently…
Phased burst errors (PBEs) are bursts of errors occurring at one or more known locations. The correction of PBEs is a classical topic in coding theory, with prominent applications such as the design of array codes for memory systems or…
The Distributed Bloom Filter is a space-efficient, probabilistic data structure designed to perform more efficient set reconciliations in distributed systems. It guarantees eventual consistency of states between nodes in a system, while…
Quantum computing is deemed to require error correction at scale to mitigate physical noise by reducing it to lower noise levels while operating on encoded logical qubits. Popular quantum error correction schemes include CSS code, of which…
As large language models (LLMs) play an increasingly important role in code generation, enhancing both correctness and efficiency has become crucial. Current methods primarily focus on correctness, often overlooking efficiency. To address…
In this paper, we present a framework for generic decoding of convolutional codes, which allows us to do cryptanalysis of code-based systems that use convolutional codes. We then apply this framework to information set decoding, study…
We extend the idea of word pieces in natural language models to machine learning tasks on opaque ids. This is achieved by applying hash functions to map each id to multiple hash tokens in a much smaller space, similarly to a Bloom filter.…
Data compression has been widely applied in many data processing areas. Compression methods use variable-size codes with the shorter codes assigned to symbols or groups of symbols that appear in the data frequently. Fibonacci coding, as a…
Due to its high data density and longevity, DNA is considered a promising medium for satisfying ever-increasing data storage needs. However, the diversity of errors that occur in DNA sequences makes efficient error-correction a challenging…
Polar codes are a class of linear block codes that provably achieves channel capacity, and have been selected as a coding scheme for $5^{\rm th}$ generation wireless communication standards. Successive-cancellation (SC) decoding of polar…
Polar codes are the first error-correcting code proven to achieve channel capacity based on infinite code length. The Successive Cancellation List Flip (SCLF) decoding algorithm was proposed by flipping an erroneous bit during the next…
Binary embedding of high-dimensional data requires long codes to preserve the discriminative power of the input space. Traditional binary coding methods often suffer from very high computation and storage costs in such a scenario. To…
In this paper we investigate the decoding of parallel turbo codes over the binary erasure channel suited for upper-layer error correction. The proposed algorithm performs on-the-fly decoding, i.e. it starts decoding as soon as the first…
Although qubit coherence times and gate fidelities are continuously improving, logical encoding is essential to achieve fault tolerance in quantum computing. In most encoding schemes, correcting or tracking errors throughout the computation…
Quantum error correction promises a viable path to fault-tolerant computations, enabling exponential error suppression when the device's error rates remain below the protocol's threshold. This threshold, however, strongly depends on the…
In this paper we investigate the role of local information in the decoding of the repetition and surface error correction codes for the protection of quantum states. Our key result is an improvement in resource efficiency when local…
A construction using the E8 lattice and Reed-Solomon codes for error-correction in flash memory is given. Since E8 lattice decoding errors are bursty, a Reed-Solomon code over GF($2^8$) is well suited. This is a type of coded modulation,…
The order statistics based list decoding techniques for linear binary block codes of small to medium block length are investigated. The construction of the list of the test error patterns is considered. The original order statistics…
To decode a short linear block code, ordered statics decoding (OSD) and/or the $A^*$ decoding are usually considered. Either OSD or the $A^*$ decoding utilizes the magnitudes of the received symbols to establish the most reliable and…