Related papers: Generic Decoding in the Cover Metric
Qualitative data analysis provides insight into the underlying perceptions and experiences within unstructured data. However, the time-consuming nature of the coding process, especially for larger datasets, calls for innovative approaches,…
We investigate dense coding by imposing various locality restrictions to our decoder by employing the resource theory of asymmetry framework. In this task, the sender Alice and the receiver Bob share an entangled state. She encodes the…
Generalized concatenated codes were introduced in the 1970s by Zinoviev. There are many types of codes in the literature that are known by other names that can be viewed as generalized concatenated codes. Examples include matrix-product…
This work shows several direct and recursive constructions of ordered covering arrays using projection, fusion, column augmentation, derivation, concatenation and cartesian product. Upper bounds on covering codes in NRT spaces are also…
Decoding sits between a language model and everything we do with it, yet it is still treated as a heuristic knob-tuning exercise. We argue decoding should be understood as a principled optimisation layer: at each token, we solve a…
Many proofs in discrete mathematics and theoretical computer science are based on the probabilistic method. To prove the existence of a good object, we pick a random object and show that it is bad with low probability. This method is…
The sum-rank metric can be seen as a generalization of both, the rank and the Hamming metric. It is well known that sum-rank metric codes outperform rank metric codes in terms of the required field size to construct maximum distance…
Typical-case computation complexity is a research topic at the boundary of computer science, applied mathematics, and statistical physics. In the last twenty years the replica-symmetry-breaking mean field theory of spin glasses and the…
Surface codes reach high error thresholds when decoded with known algorithms, but the decoding time will likely exceed the available time budget, especially for near-term implementations. To decrease the decoding time, we reduce the…
Projective Reed-Muller codes correspond to subcodes of the Reed-Muller code in which the polynomials being evaluated to yield codewords, are restricted to be homogeneous. The Generalized Hamming Weights (GHW) of a code ${\cal C}$, identify…
We propose an efficient algorithm to find a Reed-Solomon (RS) codeword at a distance within the covering radius of the code from any point in its ambient Hamming space. To the best of the authors' knowledge, this is the first attempt of its…
Neural image compression methods have seen increasingly strong performance in recent years. However, they suffer orders of magnitude higher computational complexity compared to traditional codecs, which hinders their real-world deployment.…
The likelihood encoder with a random codebook is demonstrated as an effective tool for source coding. Coupled with a soft covering lemma (associated with channel resolvability), likelihood encoders yield simple achievability proofs for…
Sum-rank metric codes have recently attracted the attention of many researchers, due to their relevance in several applications. Mathematically, the sum-rank metric is a natural generalization of both the Hamming metric and the rank metric.…
We consider the problem of covering hypersphere by a set of spherical hypercaps. This sort of problem has numerous practical applications such as error correcting codes and reverse k-nearest neighbor problem. Using the reduction of non…
Representing images by compact codes has proven beneficial for many visual recognition tasks. Most existing techniques, however, perform this coding step directly in image feature space, where the distributions of the different classes are…
Relative generalized Hamming weights (RGHWs) of a linear code respect to a linear subcode determine the security of the linear ramp secret sharing scheme based on the code. They can be used to express the information leakage of the secret…
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…
Short survey about code on the graph by example of hardware friendly quasi-cycle LDPC code. We consider two main properties of code: weight enumerator (well known from classic code theory) and Trapping sets pseudocodewords weight spectrum…
New soft- and hard decision decoding algorithms are presented for general Reed-Muller codes $\left\{\genfrac{}{}{0pt}{}{m}{r}\right\} $ of length $2^{m}$ and distance $2^{m-r}$. We use Plotkin $(u,u+v)$ construction and decompose code…