2021/07/11 by Jorge F. Silva, Silva, Jorge F., Pablo Piantanida +1
Computer Science · Engineering · #Advanced Data Compression Techniques #Advanced Image and Video Retrieval Techniques #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #Information Theory (cs.IT) #Wireless Communication Security Techniques
paper · pdf · doi:10.48550/arxiv.2107.05082
openalex publication_date 2021/07/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 (∞-alphabets) is addressed in this paper. The main results of this work offer a set of sufficient conditions (from weaker to stronger) to obtain weak minimax universality, strong minimax universality, and corresponding achievable rates of convergences for the worse-case redundancy for the family of stationary memoryless sources whose densities are dominated by an envelope function (or the envelope family) on ∞-alphabets. An important implication of these results is that universal D-semifaithful source coding is not feasible for the complete family of stationary and memoryless sources on ∞-alphabets. To demonstrate this infeasibility, a sufficient condition for the impossibility is presented for the envelope family. Interestingly, it matches the well-known impossibility condition in the context of lossless (variable-length) universal source coding. More generally, this work offers a simple description of what is needed to achieve universal D-semifaithful coding for a family of distributions Λ. This reduces to finding a collection of quantizations of the product space at different block-lengths -- reflecting the fixed distortion restriction -- that satisfy two asymptotic requirements: the first is a universal quantization condition with respect to Λ, and the second is a vanishing information radius (I-radius) condition for Λ reminiscent of the condition known for lossless universal source coding.