| Project Detail |
This proposal is for an information-theoretic study of quantization, transmission, and utilization of channel state information in state-dependent communication networks. Such networks are of paramount importance in wireless communications where the state models the time-varying fading level or channel response. In such networks the difference in throughput that state information provides is like night and day, so it is essential that it be conveyed to the receiver and, preferably, also to the transmitter. Other scenarios where state information plays a crucial role include storage devices where it models the physical state of the memory cell before it is written to, and phase-impaired communication links, where it models phase noise.In all these applications, the state is not discrete and a digital implementation requires that it be quantized before it is conveyed to the receiver and/or transmitter. This project will use information-theoretic tools to determine how to best perform this quantization in order to maximize throughput as measured by channel capacity. It will also study how the quantized information should be utilized, and how capacity depends on the quantization resolution. We shall consider state information to the receiver, to the transmitter, and to both.The quantization problem of channel states differs significantly from the analogous classical lossy data compression problem in two salient issues. The first has to do with causality: In classical data compression optimal performance is achieved by vector quantizers that describe the source sequence only after it has been observed in its entirety (or almost entirety). In this sense, they are noncausal: a symbol can be recovered only after the entire sequence has been described. This will not do for communication channels where the state information must be provided to the transmitter in a causal way: the current channel input cannot depend on the description of future channel states. The second difference is related to the fidelity criterion. Our main concern is not with how faithfully the analog state information is reproduced but with the degree to which the reconstructed state conveys the channel features that influence the channel’s capacity. This criterion leads to complicated distortion measures that are non-single-letter.To address these issues we shall begin with the discrete memoryless state-dependent channel. For this channel the state-of-the-art is to use scalar quantizers that at time-i present the encoder with a quantized version of the time-i state. We will consider the more general case, which allows the time-i description to depend on all the states up to time-i. To assess the benefits afforded by state information, we shall also study networks with a helper that observes the noise sequence and describes it with limited rate to the encoder, decoder, or both. This is a more general quantization scenario as it has no fixed description alphabet.To address storage applications, we shall also study the quantization of noncausal state information. And, in addition to the Shannon capacity, we also plan to study the Erasures-Only capacity (where the decoder must not err but may declare a failure with arbitrarily small probability) and the Identification capacity, which can be viewed as an addressing-capacity (with possible applications in the Internet of Things). Beyond communication, we shall study coordination problems and portfolio theory with quantized side information. |
