Related papers: Tighter Decoding Reliability Bound for Gallager's …
A generalization of the Reiger bound is presented for the list decoding of burst errors. It is then shown that Reed-Solomon codes attain this bound.
Noise in quantum computing is countered with quantum error correction. Achieving optimal performance will require tailoring codes and decoding algorithms to account for features of realistic noise, such as the common situation where the…
Tensor decomposition is now being used for data analysis, information compression, and knowledge recovery. However, the mathematical property of tensor decomposition is not yet fully clarified because it is one of singular learning…
We examine regular and irregular repeat-accumulate (RA) codes with repetition degrees which are all even. For these codes and with a particular choice of an interleaver, we give an upper bound on the decoding error probability of a…
We consider network coding for networks experiencing worst-case bit-flip errors, and argue that this is a reasonable model for highly dynamic wireless network transmissions. We demonstrate that in this setup prior network error-correcting…
Quantum error correction is indispensable to achieving reliable quantum computation. When quantum information is encoded redundantly, a larger Hilbert space is constructed using multiple physical qubits, and the computation is performed…
The problem of coding for networks experiencing worst-case symbol errors is considered. We argue that this is a reasonable model for highly dynamic wireless network transmissions. We demonstrate that in this setup prior network…
This paper studies random-coding error exponents of randomised list decoding, in which the decoder randomly selects $L$ messages with probabilities proportional to the decoding metric of the codewords. The exponents (or bounds) are given…
We propose a method to determine the critical noise level for decoding Gallager type low density parity check error correcting codes. The method is based on the magnetization enumerator ($\cM$), rather than on the weight enumerator ($\cW$)…
A likelihood encoder is studied in the context of lossy source compression. The analysis of the likelihood encoder is based on the soft-covering lemma. It is demonstrated that the use of a likelihood encoder together with the soft-covering…
We develop a most likely error Pauli error decoding algorithm for stabiliser codes based on general purpose integer optimisation. Using this decoder we analyse the performance of holographic codes against Pauli errors and find numerical…
In this paper, we derive Gallager's random coding error exponent for multiple-input multiple-output (MIMO) channels, assuming no channel-state information (CSI) at the transmitter and perfect CSI at the receiver. This measure gives insight…
In 1973, Gallager proved that the random-coding bound is exponentially tight for the random code ensemble at all rates, even below expurgation. This result explained that the random-coding exponent does not achieve the expurgation exponent…
The article starts with new aliasing-truncation error upper bounds in the sampling theorem for non-bandlimited stochastic signals. Then, it investigates $L_p([0,T])$ approximations of sub-Gaussian random signals. Explicit truncation error…
A new approach for estimating the Decoding Error-Probability (DEP) of LT codes with dense rows is derived by using the conditional Kovalenko's rank distribution. The estimate by the proposed approach is very close to the DEP approximated by…
In this paper q-ary Raptor codes under ML decoding are considered. An upper bound on the probability of decoding failure is derived using the weight enumerator of the outer code, or its expected weight enumerator if the outer code is drawn…
In distributed optimization problems, a technique called gradient coding, which involves replicating data points, has been used to mitigate the effect of straggling machines. Recent work has studied approximate gradient coding, which…
We introduce a technique that uses gauge fixing to significantly improve the quantum error correcting performance of subsystem codes. By changing the order in which check operators are measured, valuable additional information can be…
We present a family of algorithms, combining real-space renormalization methods and belief propagation, to estimate the free energy of a topologically ordered system in the presence of defects. Such an algorithm is needed to preserve the…
This paper presents a general methodology for deriving information-theoretic generalization bounds for learning algorithms. The main technical tool is a probabilistic decorrelation lemma based on a change of measure and a relaxation of…