Detection Performance of M-ary Relay Trees with Non-binary Message Alphabets

Details Detection Performance of M-ary Relay Trees with Non-binary Message Alphabets Detection Performance of M-ary Relay Trees with Non-binary Message Alphabets

2012-02-10

arxiv.org/abs/1202.2319v1

Computer Science

Information Theory

Submitted to SSP workshop 2012

Scientific paper

We study the detection performance of $M$-ary relay trees, where only the leaves of the tree represent sensors making measurements. The root of the tree represents the fusion center which makes an overall detection decision. Each of the other nodes is a relay node which aggregates $M$ messages sent by its child nodes into a new compressed message and sends the message to its parent node. Building on previous work on the detection performance of $M$-ary relay trees with binary messages, in this paper we study the case of non-binary relay message alphabets. We characterize the exponent of the error probability with respect to the message alphabet size $\mathcal D$, showing how the detection performance increases with $\mathcal D$. Our method involves reducing a tree with non-binary relay messages into an equivalent higher-degree tree with only binary messages.

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