Related papers: Amortized Locally Decodable Codes for Insertions a…
We construct $3$-query relaxed locally decodable codes (RLDCs) with constant alphabet size and length $\tilde{O}(k^2)$ for $k$-bit messages. Combined with the lower bound of $\tilde{\Omega}(k^3)$ of [Alrabiah, Guruswami, Kothari, Manohar,…
We investigate one possible generalization of locally recoverable codes (LRC) with all-symbol locality and availability when recovering sets can intersect in a small number of coordinates. This feature allows us to increase the achievable…
Error control is significant to network coding, since when unchecked, errors greatly deteriorate the throughput gains of network coding and seriously undermine both reliability and security of data. Two families of codes, subspace and rank…
Differential linear network coding (DLNC) is a precoding scheme for information transmission over random linear networks. By using differential encoding and decoding, the conventional approach of lifting, required for inherent channel…
Locally repairable codes (LRCs) have recently been widely used in distributed storage systems and the LRCs with $(r,\delta)$-locality ($(r,\delta)$-LRCs) attracted a lot of interest for tolerating multiple erasures. Ge et al. constructed…
Locally repairable codes (LRCs) have emerged as an important coding scheme in distributed storage systems (DSSs) with relatively low repair cost by accessing fewer non-failure nodes. Theoretical bounds and optimal constructions of LRCs have…
We construct the first (locally computable, approximately) locally list decodable codes with rate, efficiency, and error tolerance approaching the information theoretic limit, a core regime of interest for the complexity theoretic task of…
As an important coding scheme in modern distributed storage systems, locally repairable codes (LRCs) have attracted a lot of attentions from perspectives of both practical applications and theoretical research. As a major topic in the…
Over discrete memoryless channels (DMC), linear decoders (maximizing additive metrics) afford several nice properties. In particular, if suitable encoders are employed, the use of decoding algorithm with manageable complexities is…
A new construction is proposed for low density parity check (LDPC) codes using quadratic permutation polynomials over finite integer rings. The associated graphs for the new codes have both algebraic and pseudo-random nature, and the new…
Neural compression has brought tremendous progress in designing lossy compressors with good rate-distortion (RD) performance at low complexity. Thus far, neural compression design involves transforming the source to a latent vector, which…
As a medium for cold data storage, DNA stands out as it promises significant gains in storage capacity and lifetime. However, it comes with its own data processing challenges to overcome. Constrained codes over the DNA alphabet…
Linear programming (LP) decoding for low-density parity-check (LDPC) codes proposed by Feldman et al. is shown to have theoretical guarantees in several regimes and empirically is not observed to suffer from an error floor. However at low…
The linear error-correcting codes are known to be well suited for battling and correcting the burst errors caused by noise in the wireless data transmission system. However, different types of codes offer different decoding and…
Consider a distributed coding for computing problem with constant decoding locality, i.e., with a vanishing error probability, any single sample of the function can be approximately recovered by probing only constant number of compressed…
Decoding quantum error-correcting codes is a key challenge in enabling fault-tolerant quantum computation. In the classical setting, linear programming (LP) decoders offer provable performance guarantees and can leverage fast practical…
A new type of spatially coupled low-density parity-check (SC-LDPC) codes motivated by practical storage applications is presented. SC-LDPCL codes (suffix 'L' stands for locality) can be decoded locally at the level of sub-blocks that are…
We propose a two-layer coding architecture for communication of multiple users over a shared slotted medium enabling joint collision resolution and decoding. Each user first encodes its information bits with an outer code for reliability,…
Recent techniques such as retrieval-augmented generation or chain-of-thought reasoning have led to longer contexts and increased inference costs. Context compression techniques can reduce these costs, but the most effective approaches…
Channel coding aims to minimize errors that occur during the transmission of digital information from one place to another. Low-density parity-check (LDPC) codes can detect and correct transmission errors if one encodes the original…