Related papers: Relaxed Locally Correctable Codes in Computational…
Polar codes are capacity-achieving error-correcting codes with an explicit construction that can be decoded with low-complexity algorithms. In this work, we show how the state-of-the-art low-complexity decoding algorithm can be improved to…
Inspired by prior work by Tian and by Cao and Xu, this paper presents an efficient computer-aided framework to characterize the fundamental limits of coded caching systems under the constraint of linear coding. The proposed framework…
Learning, prediction, and compression are intimately connected: a model that accurately predicts the next symbol in a sequence can be coupled with a source coder to compress that sequence near its information-theoretic limit. When tokenized…
We illustrate how computer-aided methods can be used to investigate the fundamental limits of the caching systems, which are significantly different from the conventional analytical approach usually seen in the information theory…
Conventional coded computing frameworks are predominantly tailored for structured computations, such as matrix multiplication and polynomial evaluation. Such tasks allow the reuse of tools and techniques from algebraic coding theory to…
A major issue of locally repairable codes is their robustness. If a local repair group is not able to perform the repair process, this will result in increasing the repair cost. Therefore, it is critical for a locally repairable code to…
We consider transmission over a general memoryless channel, with bounded decoding complexity per bit under message passing decoding. We show that the achievable rate is bounded below capacity if there is a finite success in the decoding in…
Predictive coding has emerged as an influential normative model of neural computation, with numerous extensions and applications. As such, much effort has been put into mapping PC faithfully onto the cortex, but there are issues that remain…
We put forth new models for universal channel coding. Unlike standard codes which are designed for a specific type of channel, our most general universal code makes communication resilient on every channel, provided the noise level is below…
The security of code-based cryptography relies primarily on the hardness of decoding generic linear codes. Until very recently, all the best algorithms for solving the decoding problem were information set decoders (ISD). However, recently…
Quantum Key Distribution (QKD) enables two parties to establish a common secret key that is information-theoretically secure by transmitting random bits that are encoded as qubits and sent over a quantum channel, followed by classical…
In this work, we present the first local-decoding algorithm for expander codes. This yields a new family of constant-rate codes that can recover from a constant fraction of errors in the codeword symbols, and where any symbol of the…
Polar codes are the latest breakthrough in coding theory, as they are the first family of codes with explicit construction that provably achieve the symmetric capacity of discrete memoryless channels. Ar{\i}kan's polar encoder and…
Scaling up quantum computers to attain substantial speedups over classical computing requires fault tolerance. Conventionally, protocols for fault-tolerant quantum computation demand excessive space overheads by using many physical qubits…
Locally finding a solution to symmetry-breaking tasks such as vertex-coloring, edge-coloring, maximal matching, maximal independent set, etc., is a long-standing challenge in distributed network computing. More recently, it has also become…
To avoid prohibitive overheads in performing fault-tolerant quantum computation, the decoding problem needs to be solved accurately and at speeds sufficient for fast feedback. Existing decoding systems fail to satisfy both of these…
A fault-tolerant quantum computer will be supported by a classical decoding system interfacing with quantum hardware to perform quantum error correction. It is important that the decoder can keep pace with the quantum clock speed, within…
Over recent years, devising classification algorithms that are robust to adversarial perturbations has emerged as a challenging problem. In particular, deep neural nets (DNNs) seem to be susceptible to small imperceptible changes over test…
Locally decodable codes (LDC's) are error-correcting codes that allow recovery of individual message indices by accessing only a constant number of codeword indices. For substitution errors, it is evident that LDC's exist -- Hadamard codes…
We consider the problem of coded computing, where a computational task is performed in a distributed fashion in the presence of adversarial workers. We propose techniques to break the adversarial toleration threshold barrier previously…