Related papers: Non prefix-free codes for constrained sequences
It has been well established that wireless network coding can significantly improve the efficiency of multi-hop wireless networks. However, in a stochastic environment some of the packets might not have coding pairs, which limits the number…
Existing time series tokenization methods predominantly encode a constant number of samples into individual tokens. This inflexible approach can generate excessive tokens for even simple patterns like extended constant values, resulting in…
We introduce quantum-K ($QK$), a measure of the descriptive complexity of density matrices using classical prefix-free Turing machines and show that the initial segments of weak Solovay random and quantum Schnorr random states are…
A prefix code L satisfies the condition that no word of L is a proper prefix of another word of L. Recently, Ko, Han and Salomaa relaxed this condition by allowing a word of L to be a proper prefix of at most k words of L, for some `margin'…
We present adaptive on-line schemes for lossy encoding of individual sequences under the conditions of the Wyner-Ziv (WZ) problem. In the first part of this article, a set of fixed-rate scalar source codes with zero delay is presented. We…
We propose a method to improve traditional character-based PPM text compression algorithms. Consider a text file as a sequence of alternating words and non-words, the basic idea of our algorithm is to encode non-words and prefixes of words…
Translating characters instead of words or word-fragments has the potential to simplify the processing pipeline for neural machine translation (NMT), and improve results by eliminating hyper-parameters and manual feature engineering.…
We describe an algorithm computing an optimal prefix free code from $N$ unsorted positive integer weights in time linear in the number of machine words holding those weights. This algorithm takes advantage of common non-algebraic…
We introduce a principled probabilistic framework for reward-guided decoding in large language models, addressing the limitations of standard decoding methods that optimize token-level likelihood rather than sequence-level quality. Our…
Optimal prefix codes are studied for pairs of independent, integer-valued symbols emitted by a source with a geometric probability distribution of parameter $q$, $0{<}q{<}1$. By encoding pairs of symbols, it is possible to reduce the…
Constrained decoding enables Language Models (LMs) to produce samples that provably satisfy hard constraints. However, existing constrained-decoding approaches often distort the underlying model distribution, a limitation that is especially…
Strong typicality and the Markov lemma have been used in the proofs of several multiterminal source coding theorems. Since these two tools can be applied to finite alphabets only, the results proved by them are subject to the same…
We address the problem of delay in an arithmetic coding system. Due to the nature of the arithmetic coding process, source sequences causing arbitrarily large encoding or decoding delays exist. This phenomena raises the question of just how…
We study a Pareto-type notion of finite-block optimality for injective source codes, where two codes are compared through the full sequence of expected block lengths. As a concrete and fully analyzable test case, we revisit the four-symbol…
We derive a sufficient condition for a $k$-th order homogeneous Markov chain $\mathbf{Z}$ with finite alphabet $\mathcal{Z}$ to have a unique invariant distribution on $\mathcal{Z}^k$. Specifically, let $\mathbf{X}$ be a first-order,…
We introduce a new construction for the balancing of non-binary sequences that make use of Gray codes for prefix coding. Our construction provides full encoding and decoding of sequences, including the prefix. This construction is based on…
We investigate the conditions under which unconditional dense coding can be achieved using continuous variable entanglement. We consider the effect of entanglement impurity and detector efficiency and discuss experimental verification. We…
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…
This paper proposes a practical successive decoding scheme with finite levels for the finite-state Markov channels where there is no a priori state information at the transmitter or the receiver. The design employs either a random…
In this paper we show that combination of the minimum description length principle and a exchange-ability condition leads directly to the use of Jeffreys prior. This approach works in most cases even when Jeffreys prior cannot be…