Related papers: Reassembly Codes for the Chop-and-Shuffle Channel
The {\em insertion-deletion channel} takes as input a binary string $x \in\{0, 1\}^n$, and outputs a string $\widetilde{x}$ where some of the bits have been deleted and others inserted independently at random. In the {\em trace…
The zero-error channel capacity is the maximum asymptotic rate that can be reached with error probability exactly zero, instead of a vanishing error probability. The nature of this problem, essentially combinatorial rather than…
In the Levenshtein's sequence reconstruction problem a codeword is transmitted through $N$ channels and in each channel a set of errors is introduced to the transmitted word. In previous works, the restriction that each channel provides a…
The proliferation of creative video content has driven demand for adapting language models to handle video input and enable multimodal understanding. However, end-to-end models struggle to process long videos due to their size and…
We revisit the problem of learning from untrusted batches introduced by Qiao and Valiant [QV17]. Recently, Jain and Orlitsky [JO19] gave a simple semidefinite programming approach based on the cut-norm that achieves essentially…
Among the new techniques of Versatile Video Coding (VVC), the quadtree with nested multi-type tree (QT+MTT) block structure yields significant coding gains by providing more flexible block partitioning patterns. However, the recursive…
Current methods for compressing neural network weights, such as decomposition, pruning, quantization, and channel simulation, often overlook the inherent symmetries within these networks and thus waste bits on encoding redundant…
In this paper, we first give explicit formulas for the number of solutions of unweighted linear congruences with distinct coordinates. Our main tools are properties of Ramanujan sums and of the discrete Fourier transform of arithmetic…
Reed-Muller (RM) and polar codes are a class of capacity-achieving channel coding schemes with the same factor graph representation. Low-complexity decoding algorithms fall short in providing a good error-correction performance for RM and…
In this work, we present a new version of non-binary VT codes that are capable of correcting a single deletion or single insertion. Moreover, we provide the first known linear time algorithms that encode user messages into these codes of…
Using a mild variant of polar codes we design linear compression schemes compressing Hidden Markov sources (where the source is a Markov chain, but whose state is not necessarily observable from its output), and to decode from Hidden Markov…
Deep learning has enabled significant advances in feedback-based channel coding, yet existing learned schemes remain fundamentally limited: they employ fixed block lengths, suffer degraded performance at high rates, and cannot fully exploit…
We present a constraint-coding scheme to correct asymmetric magnitude-$1$ errors in multi-level non-volatile memories. For large numbers of such errors, the scheme is shown to deliver better correction capability compared to known…
In video coding, in-loop filters are applied on reconstructed video frames to enhance their perceptual quality, before storing the frames for output. Conventional in-loop filters are obtained by hand-crafted methods. Recently, learned…
The code that combines channel estimation and error protection has received general attention recently, and has been considered a promising methodology to compensate multi-path fading effect. It has been shown by simulations that such code…
We consider a transmitter that encodes data packets using network coding and broadcasts coded packets. A receiver employing network decoding recovers the data packets if a sufficient number of error-free coded packets are gathered. The…
A number of recent works [Goldberg 2006; O'Donnell and Servedio 2011; De, Diakonikolas, and Servedio 2017; De, Diakonikolas, Feldman, and Servedio 2014] have considered the problem of approximately reconstructing an unknown weighted voting…
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…
Sorting operation is one of the main bottlenecks for the successive-cancellation list (SCL) decoding. This paper introduces an improvement to the SCL decoding for polar and pre-transformed polar codes that reduces the number of sorting…
In this work, we consider the problem of efficient decoding of codes from insertions and deletions. Most of the known efficient codes are codes with synchronization strings which allow one to reduce the problem of decoding insertions and…