Optimal Zero-Delay Jamming over an Additive Noise Channel

Emrah Akyol, Kenneth Rose, Tamer Basar

Research output: Contribution to journalArticlepeer-review


This paper considers the problem of optimal zero-delay jamming over an additive noise channel. Building on a sequence of recent results on conditions for linearity of optimal estimation, and of optimal mappings in source-channel coding, the saddle-point solution to the jamming problem is derived for general sources and channels, without recourse to Gaussianity assumptions. The linearity conditions are shown to play a pivotal role in jamming, in the sense that the optimal jamming strategy is to effectively force both the transmitter and the receiver to default to linear mappings, i.e., the jammer ensures, whenever possible, that the transmitter and the receiver cannot benefit from non-linear strategies. This result is shown to subsume the known result for Gaussian source and channel. The conditions and general settings where such unbeatable strategy can indeed be achieved by the jammer are analyzed. Moreover, a numerical procedure is provided to approximate the optimal jamming strategy in the remaining (source-channel) cases where the jammer cannot impose linearity on the transmitter and the receiver. Next, the analysis is extended to vector sources and channels. This extension involves a new aspect of optimization: The allocation of available transmit and jamming power over source and channel components. Similar to the scalar setting, the saddle-point solution is derived using the linearity conditions in vector spaces. The optimal power allocation strategies for the jammer and the transmitter have an intuitive interpretation as the jammer allocates power according to water-filling over the channel eigenvalues, while the transmitter performs water-pouring (reverse water-filling) over the source eigenvalues.

Original languageEnglish (US)
Article number7123628
Pages (from-to)4331-4344
Number of pages14
JournalIEEE Transactions on Information Theory
Issue number8
StatePublished - Aug 2015


  • correlated jamming
  • linearity conditions
  • water-filling power allocation
  • zero-delay source-channel coding
  • zero-sum games

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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