Related papers: Coding on countably infinite alphabets
This paper deals with the problem of universal lossless coding on a countable infinite alphabet. It focuses on some classes of sources defined by an envelope condition on the marginal distribution, namely exponentially decreasing envelope…
In this paper, we study the problem of lossless universal source coding for stationary memoryless sources on countably infinite alphabets. This task is generally not achievable without restricting the class of sources over which…
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…
Motivated from the fact that universal source coding on countably infinite alphabets is not feasible, this work introduces the notion of almost lossless source coding. Analog to the weak variable-length source coding problem studied by Han…
This paper sheds light on universal coding with respect to classes of memoryless sources over a countable alphabet defined by an envelope function with finite and non-decreasing hazard rate. We prove that the auto-censuring AC code…
Universal compression of patterns of sequences generated by independently identically distributed (i.i.d.) sources with unknown, possibly large, alphabets is investigated. A pattern is a sequence of indices that contains all consecutive…
In this paper, we investigate the redundancy of universal coding schemes on smooth parametric sources in the finite-length regime. We derive an upper bound on the probability of the event that a sequence of length $n$, chosen using…
The problem of variable length and fixed-distortion universal source coding (or D-semifaithful source coding) for stationary and memoryless sources on countably infinite alphabets ($\infty$-alphabets) is addressed in this paper. The main…
Consider the set of source distributions within a fixed maximum relative entropy with respect to a given nominal distribution. Lossless source coding over this relative entropy ball can be approached in more than one way. A problem…
This paper presents prefix codes which minimize various criteria constructed as a convex combination of maximum codeword length and average codeword length or maximum redundancy and average redundancy, including a convex combination of the…
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…
We study universal compression of sequences generated by monotonic distributions. We show that for a monotonic distribution over an alphabet of size $k$, each probability parameter costs essentially $0.5 \log (n/k^3)$ bits, where $n$ is the…
The problem of joint universal source coding and identification is considered in the setting of fixed-rate lossy coding of continuous-alphabet memoryless sources. For a wide class of bounded distortion measures, it is shown that any…
We consider universal variable-to-fixed length compression of memoryless sources with a fidelity criterion. We design a dictionary codebook over the reproduction alphabet which is used to parse the source stream. Once a source subsequence…
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…
Universal source coding at short blocklengths is considered for an exponential family of distributions. The \emph{Type Size} code has previously been shown to be optimal up to the third-order rate for universal compression of all memoryless…
Many applications require data processing to be performed on individual pieces of data which are of finite sizes, e.g., files in cloud storage units and packets in data networks. However, traditional universal compression solutions would…
The minimum average number of bits need to describe a random variable is its entropy, assuming knowledge of the underlying statistics On the other hand, universal compression supposes that the distribution of the random variable, while…
We study the redundancy of universally compressing strings $X_1,\dots, X_n$ generated by a binary Markov source $p$ without any bound on the memory. To better understand the connection between compression and estimation in the Markov…
For the discrete memoryless sources with a countably infinite alphabet, we prove that for any positive integer $k$, there exists a corresponding probability interval such that if the largest symbol probability $p_{1}$ falls in this…