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This paper considers the problem of variable-length lossy source coding. The performance criteria are the excess distortion probability and the cumulant generating function of codeword lengths. We derive a non-asymptotic fundamental limit…
Current experiments are taking the first steps toward noise-resilient logical qubits. Crucially, a quantum computer must not merely store information, but also process it. A fault-tolerant computational procedure ensures that errors do not…
We introduce the class of partition-balanced families of codes, and show how to exploit their combinatorial invariants to obtain upper and lower bounds on the number of codes that have a prescribed property. In particular, we derive precise…
Data processing lower bounds on the expected distortion are derived in the finite-alphabet semi-deterministic setting, where the source produces a deterministic, individual sequence, but the channel model is probabilistic, and the decoder…
This paper studies second-order coding rates for memoryless channels with a state sequence known non-causally at the encoder. In the case of finite alphabets, an achievability result is obtained using constant-composition random coding, and…
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…
This paper proves the separation between source-network coding and channel coding in networks of noisy, discrete, memoryless channels. We show that the set of achievable distortion matrices in delivering a family of dependent sources across…
Second order asymptotics of fixed-length source coding and intrinsic randomness is discussed with a constant error constraint. There was a difference between optimal rates of fixed-length source coding and intrinsic randomness, which never…
In this paper, we consider a class of multiterminal source coding problems, each subject to distortion constraints computed using a specific, entropy-based, distortion measure. We provide the achievable rate distortion region for two cases…
Recent work has suggested that low-density generator matrix (LDGM) codes are likely to be effective for lossy source coding problems. We derive rigorous upper bounds on the effective rate-distortion function of LDGM codes for the binary…
We consider the lossy quantum source coding problem where the task is to compress a given quantum source below its von Neumann entropy. Inspired by the duality connections between the rate-distortion and channel coding problems in the…
In lossy compression, the classical tradeoff between compression rate and reconstruction distortion has traditionally guided algorithm design. However, Blau and Michaeli [5] introduced a generalized framework, known as the…
We introduce a general framework for end-to-end optimization of the rate--distortion performance of nonlinear transform codes assuming scalar quantization. The framework can be used to optimize any differentiable pair of analysis and…
The problem of variable-rate lossless data compression is considered, for codes with and without prefix constraints. Sharp bounds are derived for the best achievable compression rate of memoryless sources, when the excess-rate probability…
This paper quantifies the fundamental limits of variable-length transmission of a general (possibly analog) source over a memoryless channel with noiseless feedback, under a distortion constraint. We consider excess distortion, average…
Shannon's rate-distortion theory treats source symbols as unstructured labels. When the source is a knowledge base equipped with a logical proof system, a natural fidelity criterion is closure fidelity: a reconstruction is acceptable if it…
We study lossy source coding under a distortion measure defined by the negative log-likelihood induced by a prescribed conditional distribution $P_{X|U}$. This \emph{log-likelihood distortion} models compression settings in which the…
The penalty incurred by imposing a finite delay constraint in lossless source coding of a memoryless source is investigated. It is well known that for the so-called block-to-variable and variable-to-variable codes, the redundancy decays at…
We study the mismatched successive refinement problem where one uses Gaussian codebooks to compress an arbitrary memoryless source with successive minimum Euclidean distance encoding under the quadratic distortion measure. Specifically, we…
In this paper, we study the asymptotic performance of Abelian group codes for the lossy source coding problem for arbitrary discrete (finite alphabet) memoryless sources as well as the channel coding problem for arbitrary discrete (finite…