Related papers: Turbo Analog Error Correcting Codes Decodable By L…
Analog error correction codes, by relaxing the source space and the codeword space from discrete fields to continuous fields, present a generalization of digital codes. While linear codes are sufficient for digital codes, they are not for…
In this paper, we study turbo codes from the digital signal processing point of view by defining turbo codes over the complex field. It is known that iterative decoding and interleaving between concatenated parallel codes are two key…
In this article we extend the idea of Turbo codes onto the Real Field. The channel is taken to result in block erasures and the only noise as being that due to quantization. The decoding in this case is reduced to reconstruction of the lost…
Designing codes that combat the noise in a communication medium has remained a significant area of research in information theory as well as wireless communications. Asymptotically optimal channel codes have been developed by mathematicians…
Turbo codes are a very efficient method for communicating reliably through a noisy channel. There is no theoretical understanding of their effectiveness. In [1] they are mapped onto a class of disordered spin models. The analytical…
In this paper we investigate the decoding of parallel turbo codes over the binary erasure channel suited for upper-layer error correction. The proposed algorithm performs on-the-fly decoding, i.e. it starts decoding as soon as the first…
Neural network-based decoding methods show promise in enhancing error correction performance but face challenges with punctured codes. In particular, existing methods struggle to adapt to variable code rates or meet protocol compatibility…
We present two new algorithms for the reconstruction of turbo codes from a noisy intercepted bitstream. With these algorithms, we were able to reconstruct various turbo codes with realistic parameter sizes. To the best of our knowledge,…
It has been widely observed that there exists a fundamental trade-off between the minimum (Hamming) distance properties and the iterative decoding convergence behavior of turbo-like codes. While capacity achieving code ensembles typically…
The design of codes for feedback-enabled communications has been a long-standing open problem. Recent research on non-linear, deep learning-based coding schemes have demonstrated significant improvements in communication reliability over…
Foliated quantum codes are a resource for fault-tolerant measurement-based quantum error correction for quantum repeaters and for quantum computation. They represent a general approach to integrating a range of possible quantum error…
Two classes of turbo codes over high-order finite fields are introduced. The codes are derived from a particular protograph sub-ensemble of the (dv=2,dc=3) low-density parity-check code ensemble. A first construction is derived as a…
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 consider the problem of optimally decoding a quantum error correction code -- that is to find the optimal recovery procedure given the outcomes of partial "check" measurements on the system. In general, this problem is NP-hard. However,…
This work introduces a decoding strategy for binary self-dual codes possessing an automorphism of a specific type. The proposed algorithm is a hard decision iterative decoding scheme. The enclosed experiments show that the new decoding…
We present a theory of quantum serial turbo-codes, describe their iterative decoding algorithm, and study their performances numerically on a depolarization channel. Our construction offers several advantages over quantum LDPC codes. First,…
Turbo coding is a powerful class of forward error correcting codes, which can achieve performances close to the Shannon limit. The turbo principle can be applied to the problem of side-information source coding, and we investigate here its…
We present a novel algorithm that solves the turbo code LP decoding problem in a fininte number of steps by Euclidean distance minimizations, which in turn rely on repeated shortest path computations in the trellis graph representing the…
The design of block codes for short information blocks (e.g., a thousand or less information bits) is an open research problem that is gaining relevance thanks to emerging applications in wireless communication networks. In this paper, we…
We present an algorithm for error correction in topological codes that exploits modern machine learning techniques. Our decoder is constructed from a stochastic neural network called a Boltzmann machine, of the type extensively used in deep…