Competitive Channel-Capacity

Michael Langberg, Oron Sabag

Research output: Contribution to journalArticlepeer-review

Abstract

We consider communication over channels whose statistics are not known in full, but can be parameterized as a finite family of memoryless channels. A typical approach to address channel uncertainty is to design codes for the worst channel in the family, resulting in the well-known compound channel capacity. Although this approach is robust, it may suffer a significant loss of performance if the capacity-achieving distribution of the worst channel attains low rates over other channels. In this work, we cope with channel uncertainty through the lens of <italic>competitive analysis</italic>. The main idea is to optimize a relative metric that compares the performance of the designed code and a clairvoyant code that has access to the true channel. To allow communication rates that adapt to the channel at use, we consider rateless codes with a fixed number of message bits and random decoding times. We propose two competitive metrics: the competitive ratio between the expected rates of the two codes, and a regret defined as the difference between the expected rates. The competitive ratio, for instance, provides a percentage guarantee on the expected rate of the designed code when compared to the rate of the clairvoyant code that knows the channel at hand. Our main results are single-letter expressions for the optimal <italic>competitive-ratio</italic> and <italic>regret</italic>, expressed as a max-min or minmax optimization. Several examples illustrate the benefits of the competitive analysis approach to code design compared to the compound channel.

Original languageAmerican English
Pages (from-to)1
Number of pages1
JournalIEEE Transactions on Information Theory
DOIs
StateAccepted/In press - 2024

Bibliographical note

Publisher Copyright:
IEEE

Keywords

  • Codes
  • Compounds
  • Decoding
  • Optimization
  • Time measurement
  • Transmitters
  • Uncertainty

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