Chatting in distributed quantization networks

Abstract

Abstract-Several key results in source coding offer the intuition that distributed encoding via vector-quantize-and-bin is only slightly suboptimal to joint encoding and oftentimes is just as good. However, when source acquisition requires the blocklength to be small, collaboration between sensors can greatly reduce distortion. For a distributed acquisition network where sensors are allowed to "chat" using a side channel, we provide exact characterization of distortion performance and quantizer design in the high-resolution (low-distortion) regime using a framework called distributed functional scalar quantization (DFSQ). The key result is that chatting can dramatically improve performance even when the intersensor communication is at very low rate. We also solve the rate allocation problem when communication links have heterogeneous costs and provide examples to demonstrate that this theory predicts performance at practical communication rates.

Distributed Quantization Networks

“…Although Lemma 2 is always true, we emphasize that its effectiveness in predicting the proper cost allocation in a distributed network is only rigorously shown for high cost (i.e. high rate) due to its dependence on (8). However, it can be experimentally verified that costs corresponding to moderate communication rates still yield near-optimal allocations.…”

“…When the computation induces the sensitivity to be 0 on some subintervals of the support, the high-resolution assumptions are violated and the asymptotic distortion performance may not be described by (8). This issue is addressed by carefully coding when the source is in such a "don't-care" interval [4, Section VII] and then applying traditional high-resolution theory to the remaining support.…”

“…Moreover, this network reveals some surprising insights into the behavior of chatting. While this paper restricts its attention solely to the maximum computation, more examples are discussed in [8].…”

“…Finally, we recognize that intersensor communication can occur on low-cost channels and solve the rate allocation problem in networks with heterogeneous links and different costs of transmission. The basic concepts of this work were introduced in [8]; this paper provides more complete and definitive coverage, including more results on rate allocation, a discussion on generalizing chatting messages, and details on the impact of various optimizations. We begin by introducing related work, notation and prerequisite results in Section II.…”

Rate loss in distributed functional source coding

“…In prior work, we demonstrated how intersensor interaction can affect the design of scalar quantizers in distributed architectures [19]. One extension is to determine the rateloss bounds for this generalization, building off rate-distortion results in [20].…”