Related papers: From Bit to Block: Decoding on Erasure Channels
Locally repairable codes (LRCs) were originally introduced to enable efficient recovery from erasures in distributed storage systems by accessing only a small number of other symbols. While their structural properties-such as bounds and…
Recently, the authors showed that Reed-Muller (RM) codes achieve capacity on binary memoryless symmetric (BMS) channels with respect to bit error rate. This paper extends that work by showing that RM codes defined on non-binary fields,…
Bounds on the reliability function for the discrete memoryless relay channel are derived using the method of types. Two achievable error exponents are derived based on partial decode-forward and compress-forward which are well-known…
This paper shows that a class of codes such as Reed-Muller (RM) codes have vanishing bit-error probability below capacity on symmetric channels. The proof relies on the notion of `camellia codes': a class of symmetric codes decomposable…
Motivated by recommendation systems, we consider the problem of estimating block constant binary matrices (of size $m \times n$) from sparse and noisy observations. The observations are obtained from the underlying block constant matrix…
We derive a new upper bound on the reliability function for channel coding over discrete memoryless channels. Our bounding technique relies on two main elements: (i) adding an auxiliary genie-receiver that reveals to the original receiver a…
Fair threshold estimation for bivariate bicycle (BB) codes on the quantum erasure channel runs into two recurring problems: decoder-baseline unfairness and the conflation of finite-size pseudo-thresholds with true asymptotic thresholds. We…
In this paper, by treating Reed-Muller (RM) codes as a special class of low-density parity-check (LDPC) codes and assuming that sub-blocks of the parity-check matrix are randomly interleaved to each other as Gallager's codes, we present a…
The performance of maximum-likelihood (ML) decoded binary linear block codes is addressed via the derivation of tightened upper bounds on their decoding error probability. The upper bounds on the block and bit error probabilities are valid…
Designing a practical, low complexity, close to optimal, channel decoder for powerful algebraic codes with short to moderate block length is an open research problem. Recently it has been shown that a feed-forward neural network…
We consider communication over memoryless channels using low-density parity-check code ensembles above the iterative (belief propagation) threshold. What is the computational complexity of decoding (i.e., of reconstructing all the typical…
We study the channel coding problem when errors and uncertainty occur in the encoding process. For simplicity we assume the channel between the encoder and the decoder is perfect. Focusing on linear block codes, we model the encoding…
Surface codes are among the best candidates to ensure the fault-tolerance of a quantum computer. In order to avoid the accumulation of errors during a computation, it is crucial to have at our disposal a fast decoding algorithm to quickly…
Error correction code is a major part of the communication physical layer, ensuring the reliable transfer of data over noisy channels. Recently, neural decoders were shown to outperform classical decoding techniques. However, the existing…
We establish a general framework for construction of small ensembles of capacity achieving linear codes for a wide range of (not necessarily memoryless) discrete symmetric channels, and in particular, the binary erasure and symmetric…
We consider the problem of coded distributed computing where a large linear computational job, such as a matrix multiplication, is divided into $k$ smaller tasks, encoded using an $(n,k)$ linear code, and performed over $n$ distributed…
This paper investigates two distinct types of block errors - undetected errors (confusions) and erasures - in additive white Gaussian noise (AWGN) channels with error-bounded block decoders operating in the finite blocklength (FBL) regime.…
We investigate the duality of the binary erasure channel (BEC) and the binary defect channel (BDC). This duality holds for channel capacities, capacity achieving schemes, minimum distances, and upper bounds on the probability of failure to…
Low-depth random circuit codes possess many desirable properties for quantum error correction but have so far only been analyzed in the code capacity setting where it is assumed that encoding gates and syndrome measurements are noiseless.…
Reed-Muller (RM) codes are known for their good maximum likelihood (ML) performance in the short block-length regime. Despite being one of the oldest classes of channel codes, finding a low complexity soft-input decoding scheme is still an…