Related papers: Error Correcting Coding for a Non-symmetric Ternar…
We introduce a new analysis technique to derive a single-letter upper bound on the mismatch capacity of a stationary, single-user, memoryless channel with a decoding metric $q$. Our bound is obtained by considering a multicast transmission…
Fault tolerance is a prerequisite for scalable quantum computing. Architectures based on 2D topological codes are effective for near-term implementations of fault tolerance. To obtain high performance with these architectures, we require a…
Exponential error bounds achievable by universal coding and decoding are derived for frame-asynchronous discrete memoryless %asynchronous multiple access channels with two senders, via the method of subtypes, a refinement of the method of…
This paper presents encoding and decoding algorithms for several families of optimal rank metric codes whose codes are in restricted forms of symmetric, alternating and Hermitian matrices. First, we show the evaluation encoding is the right…
This paper introduces a new approach to proving that a sequence of deterministic linear codes achieves capacity on an erasure channel under maximum a posteriori decoding. Rather than relying on the precise structure of the codes, this…
In this work, we investigate the problem of neural-based error correction decoding, and more specifically, the new so-called syndrome-based decoding technique introduced to tackle scalability in the training phase for larger code sizes. We…
Quantum error correction offers a promising path for performing quantum computations with low errors. Although a fully fault-tolerant execution of a quantum algorithm remains unrealized, recent experimental developments, along with…
Error correcting codes play a central role in digital communication, ensuring that transmitted information can be accurately reconstructed despite channel impairments. Recently, autoencoder (AE) based approaches have gained attention for…
In this paper, we design the optimal rate capacity approaching irregular Low-Density Parity-Check code ensemble over Binary Erasure Channel, by using practical Semi-Definite Programming approach. Our method does not use any relaxation or…
In this paper, a novel decoding algorithm for low-density parity-check (LDPC) codes based on convex optimization is presented. The decoding algorithm, called interior point decoding, is designed for linear vector channels. The linear vector…
In this paper, we develop a new decoding algorithm of a binary linear codes for symbol-pair read channels. Symbol-pair read channel has recently been introduced by Cassuto and Blaum to model channels with high write resolution but low read…
We consider upper bounds on the error probability in channel coding. We derive an improved maximum-likelihood union bound, which takes into account events where the likelihood of the correct codeword is tied with that of some competitors.…
Upper and lower bounds on the error probability of linear codes under maximum-likelihood (ML) decoding are shortly surveyed and applied to ensembles of codes on graphs. For upper bounds, focus is put on Gallager bounding techniques and…
In this paper, we study binary and ternary matrices that are used for CDMA applications that are injective on binary or ternary user vectors. In other words, in the absence of additive noise, the interference of overloaded CDMA can be…
We recently showed in [1] the superiority of certain structured coding matrices ensembles (such as partial row-orthogonal) for sparse superposition codes when compared with purely random matrices with i.i.d. entries, both…
This paper considers the problem of covert communication with mismatched decoding, in which a sender wishes to reliably communicate with a receiver whose decoder is fixed and possibly sub-optimal, and simultaneously to ensure that the…
Motivated by applications of biometric identification and content identification systems, we consider the problem of random coding for channels, where each codeword undergoes lossy compression (vector quantization), and where the decoder…
This paper is motivated by the problem of error control in network coding when errors are introduced in a random fashion (rather than chosen by an adversary). An additive-multiplicative matrix channel is considered as a model for random…
Error exponents characterize the exponential decay, when increasing message length, of the probability of error of many error-correcting codes. To tackle the long standing problem of computing them exactly, we introduce a general,…
Surface codes are a promising method of quantum error correction and the basis of many proposed quantum computation implementations. However, their efficient decoding is still not fully explored. Recently, approaches based on machine…