相关论文: Prefix Codes for Power Laws with Countable Support
Grammar-based compression is a popular and powerful approach to compressing repetitive texts but until recently its relatively poor time-space trade-offs during real-life construction made it impractical for truly massive datasets such as…
Universal fixed-to-variable lossless source coding for memoryless sources is studied in the finite blocklength and higher-order asymptotics regimes. Optimal third-order coding rates are derived for general fixed-to-variable codes and for…
Sequential probability assignment and universal compression go hand in hand. We propose sequential probability assignment for non-binary (and large alphabet) sequences with empirical distributions whose parameters are known to be bounded…
Polarization-adjusted convolutional (PAC) codes combine the polar and convolutional transformations to enhance the distance properties of polar codes. They offer a performance very close to the finite length information-theoretic bounds for…
Adaptive coding faces the following problem: given a collection of source classes such that each class in the collection has non-trivial minimax redundancy rate, can we design a single code which is asymptotically minimax over each class in…
We present new lower and upper bounds for the compression rate of binary prefix codes optimized over memoryless sources according to two related exponential codeword length objectives. The objectives explored here are exponential-average…
In this paper we study the adaptive prefix coding problem in cases where the size of the input alphabet is large. We present an online prefix coding algorithm that uses $O(\sigma^{1 / \lambda + \epsilon}) $ bits of space for any constants…
The tree based representation described in this paper, hereditarily binary numbers, applies recursively a run-length compression mechanism that enables computations limited by the structural complexity of their operands rather than by their…
Code Division Multiple Access (CDMA) in which the spreading code assignment to users contains a random element has recently become a cornerstone of CDMA research. The random element in the construction is particular attractive as it…
Language Reasoning Models (LRMs) achieve strong performance by scaling test-time computation but often suffer from ``overthinking'', producing excessively long reasoning traces that increase latency and memory usage. Existing LRMs typically…
This paper presents lossless prefix codes optimized with respect to a pay-off criterion consisting of a convex combination of maximum codeword length and average codeword length. The optimal codeword lengths obtained are based on a new…
We study the new problem of Huffman-like codes subject to individual restrictions on the code-word lengths of a subset of the source words. These are prefix codes with minimal expected code-word length for a random source where additionally…
Efficient methods for storing and querying are critical for scaling high-order n-gram language models to large corpora. We propose a language model based on compressed suffix trees, a representation that is highly compact and can be easily…
Coded computing is a distributed paradigm that uses coding theory to introduce \textit{redundancy} and overcome bottlenecks in large-scale systems. In the same vein, randomized numerical linear algebra employs probabilistic methods to…
This paper presents new lower and upper bounds for the compression rate of binary prefix codes optimized over memoryless sources according to various nonlinear codeword length objectives. Like the most well-known redundancy bounds for…
Rank modulation has been recently proposed as a scheme for storing information in flash memories. While rank modulation has advantages in improving write speed and endurance, the current encoding approach is based on the "push to the top"…
A new method for constructing minimum-redundancy binary prefix codes is described. Our method does not explicitly build a Huffman tree; instead it uses a property of optimal prefix codes to compute the codeword lengths corresponding to the…
We consider a variant of the channel simulation problem with a single input and multiple outputs, where Alice observes a probability distribution $P$ from a set of prescribed probability distributions $\mathbb{\mathcal{P}}$, and sends a…
This paper is concerned with algorithms for prediction of discrete sequences over a finite alphabet, using variable order Markov models. The class of such algorithms is large and in principle includes any lossless compression algorithm. We…
The power law is useful in describing count phenomena such as network degrees and word frequencies. With a single parameter, it captures the main feature that the frequencies are linear on the log-log scale. Nevertheless, there have been…