Noise prediction for channels with side information at the transmitter

Uri Erez*, Ram Zamir

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The computation of channel capacity with side information at the transmitter side (but not at the receiver side) requires, in general, extension of the input alphabet to a space of strategies, and is often hard. We consider the special case of a discrete memoryless modulo-additive noise channel Y = X + Zs, where the encoder observes causally the random state S G S that governs the distribution of the noise ZS. We show that the capacity of this channel is given by C = log |X| - mint:S→X H(ZS - t(S)). This capacity is realized by a state-independent code, followed by a shift by the "noise prediction" tmin(S) that minimizes the entropy of Zs -t(S). If the set of conditional noise distributions {p( z \s), s ∈ S} is such that the optimum predictor tmin(·) is independent of the state weights, then C is also the capacity for a noncausal encoder, that observes the entire state sequence in advance. Furthermore, for this case we also derive a simple formula for the capacity when the state process has memory.

Original languageEnglish
Pages (from-to)1610-1617
Number of pages8
JournalIEEE Transactions on Information Theory
Issue number4
StatePublished - 2000


  • Optimum transmitter
  • Prediction with minimum error entropy
  • Side information
  • Time-varying channels


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