The classical problem of reliable point-to-point digital communication can be considered as wanting to achieve a very low probability of error while keeping the rate high and the total power consumption small. Traditional information-theoretic analysis uses explicit models for the communication channel to study the power spent in transmission. The resulting bounds are expressed using `waterfall' curves that convey the revolutionary idea that unboundedly low probabilities of bit-error are attainable using only finite transmit power.
However, practitioners have long observed that the decoder complexity, and hence the total power consumption, goes up when attempting to use sophisticated codes that operate close to the Shannon waterfall curve. This is especially true when short-range communication is considered. This talk asks the question of what "capacity-achieving" should mean if we have to care about total power rather than just transmitter power.
Power consumption is thus considered to be the natural metric for complexity. Classical results are reinterpreted in this context and are shown to imply that neither classical dense linear codes with ML decoding nor convolutional codes can be capacity achieving in any reasonable sense. An explicit model is given for the power consumption of an idealized decoder that allows for extreme parallelism in implementation. This decoder architecture is in the spirit of message passing and iterative decoding for sparse-graph codes.
Generalized sphere-packing arguments are used to derive lower bounds on the decoding power needed for any possible code given only the gap from the Shannon limit and the desired average probability of bit error. As the gap goes to zero, the energy per bit spent in decoding is shown to go to infinity. This suggests that to optimize total power, the transmitter should operate at a power that is strictly above the minimum demanded by the Shannon capacity. The lower bound is also plotted to show an unavoidable tradeoff between the average bit-error probability and the total power used in transmission and decoding. In the spirit of conventional waterfall curves, we call these `waterslide' curves.
(This is joint work with my student Pulkit Grover)
BiographyAnant Sahai (BS '94 UC Berkeley, MS '96 MIT, PhD '01 MIT) joined the Department of Electrical Engineering and Computer Sciences at the University of California at Berkeley in 2002 as an Assistant Professor. He is a member of the Berkeley Wireless Research Center (BWRC) and the Wireless Foundations Center (WiFo). In 2001, he spent a year at the wireless startup Enuvis developing adaptive signal processing algorithms for extremely sensitive GPS receivers implemented using software defined radio. Prior to that, he was a graduate student at the Laboratory for Information and Decision Systems (LIDS) at the Massachusetts Institute of Technology (MIT). His research interests are in wireless communication, signal processing, and information theory. He is particularly interested in delay, feedback, and complexity from an information-theoretic perspective and in cognitive radio from a signal-processing perspective.