Bits through deterministic relay cascades with half-duplex constraint

Tobias Lutz, Christoph Hausl, Ralf Kötter

Research output: Contribution to journalArticlepeer-review

16 Scopus citations

Abstract

Consider a relay cascade, i.e., a network where a source node, a sink node and a certain number of intermediate source/relay nodes are arranged on a line and where adjacent node pairs are connected by error-free $(q+1)$ -ary pipes. Suppose the source and a subset of the relays wish to communicate independent information to the sink under the condition that each relay in the cascade is half-duplex constrained. A coding scheme is developed which transfers information by an information-dependent allocation of the transmission and reception slots of the relays. The coding scheme requires synchronization on the symbol level through a shared clock. The coding strategy achieves capacity for a single source. Numerical values for the capacity of cascades of various lengths are provided, and the capacities are significantly higher than the rates which are achievable with a predetermined time-sharing approach. If the cascade includes a source and a certain number of relays with their own information, the strategy achieves the cut-set bound when the rates of the relay sources fall below certain thresholds. For cascades composed of an infinite number of half-duplex constrained relays and a single source, we derive an explicit capacity expression. Remarkably, the capacity in bits/use for $q=1$ is equal to the logarithm of the golden ratio, and the capacity for $q=2$ is 1 bit/use.

Original languageEnglish
Article number6121995
Pages (from-to)369-381
Number of pages13
JournalIEEE Transactions on Information Theory
Volume58
Issue number1
DOIs
StatePublished - Jan 2012

Keywords

  • Capacity
  • capacity region
  • constrained coding
  • golden ratio
  • half-duplex constraint
  • method of types
  • network coding
  • relay networks
  • timing

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