Related papers: Balanced Permutation Codes
Designing neural network architectures is a task that lies somewhere between science and art. For a given task, some architectures are eventually preferred over others, based on a mix of intuition, experience, experimentation and luck. For…
We introduce a notion of compatibility between constraint encoding and compositional structure. Phrased in the language of category theory, it is given by a "composable constraint encoding". We show that every composable constraint encoding…
We show that iterative coding systems can not surpass capacity using only quantities which naturally appear in density evolution. Although the result in itself is trivial, the method which we apply shows that in order to achieve capacity…
The $r$-rounds Even-Mansour block cipher is a generalization of the well known Even-Mansour block cipher to $r$ iterations. Attacks on this construction were described by Nikoli\'c et al. and Dinur et al., for $r = 2, 3$. These attacks are…
Token prediction stability remains a challenge in autoregressive generative models, where minor variations in early inference steps often lead to significant semantic drift over extended sequences. A structured modulation mechanism was…
Multimodal learning has gained attention for its capacity to integrate information from different modalities. However, it is often hindered by the multimodal imbalance problem, where certain modality dominates while others remain…
Concatenating quantum error correction codes scales error correction capability by driving logical error rates down double-exponentially across levels. However, the noise structure shifts under concatenation, making it hard to choose an…
A novel permutation decoding method for Reed-Muller codes is presented. The complexity and the error correction performance of the suggested permutation decoding approach are similar to that of the recursive lists decoder. It is…
Different ways to describe a permutation, as a sequence of integers, or a product of Coxeter generators, or a tree, give different choices to define a simple permutation. We recollect few of them, define new types of simple permutations,…
A pattern class is a set of permutations closed under the formation of subpermutations. Such classes can be characterised as those permutations not involving a particular set of forbidden permutations. A simple collection of necessary and…
This work addresses the problem of assigning periodic tasks to workers in a balanced way, i.e., so that each worker performs every task with the same frequency over the long term. The input consists of a list of tasks to be repeated weekly…
Modular battery integrated converters or so called dynamically reconfigurable battery packs are expanding into emerging applications, including electromobility and grid storage. Although they offer many degrees of freedom, the state of the…
We give a general constructive proof for hierarchical coordinatizations (Lagrange Decompositions) of permutation groups. The generalization originates from the investigation of how the subgroup chains of finite permutation groups yield…
The Load-Balanced Router architecture has received a lot of attention because it does not require centralized scheduling at the internal switch fabrics. In this paper we reexamine the architecture, motivated by its potential to turn off…
Fault-tolerant capacities quantify the ability of a quantum channel to reliably transmit information when every component of the encoding and decoding procedure is noisy. Earlier work analyzed achievable communication rates under such noise…
Permutation codes were extensively studied in order to correct different types of errors for the applications on power line communication and rank modulation for flash memory. In this paper, we introduce the neural network decoders for…
We develop a method using parameterized linear equations to define trading mechanisms in market design models. Our method adeptly addresses challenges arising from factors such as complex endowments or coarse priorities, while offering…
In this paper, we formally define and analyze the class of noisy permutation channels. The noisy permutation channel model constitutes a standard discrete memoryless channel (DMC) followed by an independent random permutation that reorders…
Let n be an even positive integer and F be the field \GF(2). A word in F^n is called balanced if its Hamming weight is n/2. A subset C \subseteq F^n$ is called a balancing set if for every word y \in F^n there is a word x \in C such that y…
A simple binary model to compute the degree of balancedness in the output sequence of LFSR-combinational generators has been developed. The computational method is based exclusively on the handling of binary strings by means of logic…