Related papers: Algorithmic Polarization for Hidden Markov Models
-We develop a polar coding scheme for empirical coordination in a two-node network with a noisy link in which the input and output signals have to be coordinated with the source and the reconstruction. In the case of non-causal encoding and…
Polarization-adjusted convolutional (PAC) codes have recently emerged as a promising class of error-correcting codes, achieving near-capacity performance particularly in the short block-length regime. In this paper, we propose an enhanced…
Progress in designing channel codes has been driven by human ingenuity and, fittingly, has been sporadic. Polar codes, developed on the foundation of Arikan's polarization kernel, represent the latest breakthrough in coding theory and have…
Despite their high accuracy, complex neural networks demand significant computational resources, posing challenges for deployment on resource constrained devices such as mobile phones and embedded systems. Compression algorithms have been…
Polar codes are capacity-achieving error-correcting codes with an explicit construction that can be decoded with low-complexity algorithms. In this work, we show how the state-of-the-art low-complexity decoding algorithm can be improved to…
We propose a scheme that universally achieves the smallest possible compression rate for a class of sources with side information, and develop an application of this result for a joint source channel coding problem over a broadcast channel.
In the context of the compressed sensing problem, we propose a new ensemble of sparse random matrices which allow one (i) to acquire and compress a {\rho}0-sparse signal of length N in a time linear in N and (ii) to perfectly recover the…
We consider communication over a noisy network under randomized linear network coding. Possible error mechanism include node- or link- failures, Byzantine behavior of nodes, or an over-estimate of the network min-cut. Building on the work…
The recently introduced polar codes constitute a breakthrough in coding theory due to their capacityachieving property. This goes hand in hand with a quasilinear construction, encoding, and successive cancellation list decoding procedures…
We derive novel upper and lower finite-length bounds of the error probability in joint source-channel coding when the source obeys an ergodic Markov process and the channel is a Markovian additive channel or a Markovian conditional additive…
Neural compression offers a domain-agnostic approach to creating codecs for lossy or lossless compression via deep generative models. For sequence compression, however, most deep sequence models have costs that scale with the sequence…
We study the problem of multi-bit watermarking for large language models (LLMs). We introduce a block-autoregressive model inspired by multi-token prediction, in which the encoder has limited non-causal access to token distributions within…
In the Shannon lecture at the 2019 International Symposium on Information Theory (ISIT), Ar{\i}kan proposed to employ a one-to-one convolutional transform as a pre-coding step before the polar transform. The resulting codes of this…
In this paper, we study the lossless analog compression for i.i.d. nonsingular signals via the polarization-based framework. We prove that for nonsingular source, the error probability of maximum a posteriori (MAP) estimation polarizes…
We present a scheme for magic state distillation using punctured polar codes. Our results build on some recent work by Bardet et al. (ISIT, 2016) who discovered that polar codes can be described algebraically as decreasing monomial codes.…
Product codes are widespread in optical communications, thanks to their high throughput and good error-correction performance. Systematic polar codes have been recently considered as component codes for product codes. In this paper, we…
Error-correcting codes that admit local decoding and correcting algorithms have been the focus of much recent research due to their numerous theoretical and practical applications. An important goal is to obtain the best possible tradeoffs…
It was recently shown that the lossless compression of a single source $X^n$ is achievable with a notion of strong locality; any $X_i$ can be decoded from a constant number of compressed bits, with a vanishing in $n$ probability of error.…
Polar codes are a class of capacity-achieving error correcting codes that have been selected for use in enhanced mobile broadband in the 3GPP 5th generation (5G) wireless standard. Most polar code research examines the original Arikan polar…
Current deterministic algorithms for the construction of polar codes can only be argued to be practical for channels with small input alphabet sizes. In this paper, we show that any construction algorithm for channels with moderate input…