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 language | English |
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Article number | 6121995 |
Pages (from-to) | 369-381 |
Number of pages | 13 |
Journal | IEEE Transactions on Information Theory |
Volume | 58 |
Issue number | 1 |
DOIs | |
State | Published - Jan 2012 |
Keywords
- Capacity
- capacity region
- constrained coding
- golden ratio
- half-duplex constraint
- method of types
- network coding
- relay networks
- timing