Related papers: It'll probably work out: improved list-decoding th…
In combinatorics, the probabilistic method is a very powerful tool to prove the existence of combinatorial objects with interesting and useful properties. Explicit constructions of objects with such properties are often very difficult, or…
We study coding schemes for error correction in interactive communications. Such interactive coding schemes simulate any $n$-round interactive protocol using $N$ rounds over an adversarial channel that corrupts up to $\rho N$ transmissions.…
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,…
We explore the relationship between polar and RM codes and we describe a coding scheme which improves upon the performance of the standard polar code at practical block lengths. Our starting point is the experimental observation that RM…
In addition to a proposed codeword, error correction decoders that provide blockwise soft output (SO) return an estimate of the likelihood that the decoding is correct. Following Forney, such estimates are traditionally only possible for…
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…
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…
A convolutional code $\C$ over $\ZZ[D]$ is a $\ZZ[D]$-submodule of $\ZZN[D]$ where $\ZZ[D]$ stands for the ring of polynomials with coefficients in $\ZZ$. In this paper, we study the list decoding problem of these codes when the…
We consider coding schemes for computationally bounded channels, which can introduce an arbitrary set of errors as long as (a) the fraction of errors is bounded with high probability by a parameter $p$ and (b) the process which adds the…
The Reed-Muller (RM) code encoding $n$-variate degree-$d$ polynomials over ${\mathbb F}_q$ for $d < q$, with its evaluation on ${\mathbb F}_q^n$, has relative distance $1-d/q$ and can be list decoded from a $1-O(\sqrt{d/q})$ fraction of…
In this paper, we use reinforcement learning to find effective decoding strategies for binary linear codes. We start by reviewing several iterative decoding algorithms that involve a decision-making process at each step, including…
We consider a large-scale matrix multiplication problem where the computation is carried out using a distributed system with a master node and multiple worker nodes, where each worker can store parts of the input matrices. We propose a…
The decoding error probability of codes is studied as a function of their block length. It is shown that the existence of codes with a polynomially small decoding error probability implies the existence of codes with an exponentially small…
An index code is said to be locally decodable if each receiver can decode its demand using its side information and by querying only a subset of the transmitted codeword symbols instead of observing the entire codeword. Local decodability…
A falling rule list is a probabilistic decision list for binary classification, consisting of a series of if-then rules with antecedents in the if clauses and probabilities of the desired outcome ("1") in the then clauses. Just as in a…
Codes are widely used in many engineering applications to offer robustness against noise. In large-scale systems there are several types of noise that can affect the performance of distributed machine learning algorithms -- straggler nodes,…
In steganography, we always hope to maximize the embedding payload subject to an upper-bounded distortion. We need suitable distortion measurement to evaluate the embedding impact. However, different distortion functions exposes different…
A significant effort has been made to train neural networks that replicate algorithmic reasoning, but they often fail to learn the abstract concepts underlying these algorithms. This is evidenced by their inability to generalize to data…
We present an approach to showing that a linear code is resilient to random errors. We use this approach to obtain decoding results for both transitive codes and Reed-Muller codes. We give three kinds of results about linear codes in…
List recovery of error-correcting codes has emerged as a fundamental notion with broad applications across coding theory and theoretical computer science. Folded Reed-Solomon (FRS) and univariate multiplicity codes are explicit…