Related papers: Error Correction for Cooperative Data Exchange
Information exchange in multi-agent systems improves the cooperation among agents, especially in partially observable settings. In the real world, communication is often carried out over imperfect channels. This requires agents to handle…
In this work we investigate codes in $\mathbb{Z}_{2^m}^n$ that can correct errors that occur in just one coordinate of the codeword, with a magnitude of up to a given parameter $t$. We will show upper bounds on these cross codes, derive…
Topological error correction--a novel method to actively correct errors based on cluster states with topological properties--has the highest order of tolerable error rates known to date (10^{-2}). Moreover, the scheme requires only…
We propose a network-coding based scheme to protect multiple bidirectional unicast connections against adversarial errors and failures in a network. The network consists of a set of bidirectional primary path connections that carry the…
The problem of computing a linear combination of sources over a multiple access channel is studied. Inner and outer bounds on the optimal tradeoff between the communication rates are established when encoding is restricted to random…
Matrix multiplication over the real field constitutes a foundational operation in the training of deep learning models, serving as a computational cornerstone for both forward and backward propagation processes. However, the presence of…
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,…
This paper proposes a method for designing error correction codes by combining a known coding scheme with an autoencoder. Specifically, we integrate an LDPC code with a trained autoencoder to develop an error correction code for intractable…
We consider the problem of block-coded communication, where in each block, the channel law belongs to one of two disjoint sets. The decoder is aimed to decode only messages that have undergone a channel from one of the sets, and thus has to…
In this paper, we discuss a construction method of quantum deletion error-correcting codes. First of all, we define deletion errors for quantum states, an encoder, a decoder, and two conditions which is expressed by only the combinatorial…
Many proposals for quantum information processing are subject to detectable loss errors. In this paper, we show that topological error correcting codes, which protect against computational errors, are also extremely robust against losses.…
Coupling cyber and physical systems gives rise to numerous engineering challenges and opportunities. An important challenge is the contagion of failure from one system to another, which can lead to large-scale cascading failures. However,…
Consider a receiver in a multi-user network that wishes to decode several messages. Simultaneous joint typicality decoding is one of the most powerful techniques for determining the fundamental limits at which reliable decoding is possible.…
Erasures are the primary type of errors in physical systems dominated by leakage errors. While quantum error correction (QEC) using stabilizer codes can combat erasure errors, it remains unknown which constructions achieve capacity…
This paper studies channel coding for the discrete memoryless multiple-access channel with a given (possibly suboptimal) decoding rule. A multi-letter successive decoding rule depending on an arbitrary non-negative decoding metric is…
We investigate the relation between the girth and the guaranteed error correction capability of $\gamma$-left regular LDPC codes when decoded using the bit flipping (serial and parallel) algorithms. A lower bound on the number of variable…
We give a centralized deterministic algorithm for constructing linear network error-correcting codes that attain the Singleton bound of network error-correcting codes. The proposed algorithm is based on the algorithm by Jaggi et al. We give…
Mitigating errors in computing and communication systems has seen a great deal of research since the beginning of the widespread use of these technologies. However, as we develop new methods to do computation or communication, we also need…
A linear-programming decoder for \emph{nonbinary} expander codes is presented. It is shown that the proposed decoder has the maximum-likelihood certificate properties. It is also shown that this decoder corrects any pattern of errors of a…
Error-correcting codes and related combinatorial constructs play an important role in several recent (and old) results in computational complexity theory. In this paper we survey results on locally-testable and locally-decodable…