Bits Through Relay Cascades with Half-Duplex Constraint

Consider a relay cascade, i.e. a network where the source node, the sink node and a certain number of intermediate relay nodes are arranged in a line. We assume that adjacent node pairs are connected by error-free (q + 1)-ary pipes. The following communication scenario is treated. The source and a subset of the relays wish to communicate independent information to a common sink under the condition that each relay in the cascade is half-duplex constrained. We introduce a simple channel model for half-duplex constrained links and provide a coding scheme which transfers information by an information-dependent, nondeterministic allocation of the transmission and reception slots of the relays. The coding scheme requires synchronization on the symbol level through a shared clock. In the case of a relay cascade with a single source, the coding strategy is capacity achieving. Numerical values for the capacity of cascades of various lengths are provided, and it turns out that the capacities are significantly higher than the rates which are achievable with a deterministic 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 individual thresholds. Hence, a partial characterization of the boundary of the capacity region follows. 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 for q = 1 is equal to the logarithm of the golden ratio. We finally show that the proposed coding strategy is superior to network coding in the case of the wireless, half-duplex constrained butterfly network. Index Terms Half-duplex constraint, relay networks, network coding, timing, constrained coding, capacity, capacity region, method of types, golden ratio.