Bits Through Deterministic Relay Cascades with Half-Duplex Constraint

TL;DR

This paper introduces a novel coding scheme for relay cascades with half-duplex constraints, achieving capacity through synchronized, information-dependent slot allocation, significantly outperforming traditional time-sharing methods.

Contribution

The paper develops a capacity-achieving coding strategy for half-duplex relay cascades that uses synchronized, information-dependent transmission and reception scheduling.

Findings

Capacity exceeds traditional time-sharing rates.

Achieves cut-set bound under certain conditions.

Explicit capacity for infinite relay cascades with single source.

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.