Very Noisy channels (such as the wideband gaussian channel well-known in deep space communications) have the interesting property that although the maximum number of bits transmitted per symbol is close to zero, the maximum number of bits transmitted per second is not! Furthermore, recent results on the ultimate limits of information density indicate that some channels perform better when pushed to their very noisy limit.
We present a general mathematical model of Very Noisy channels which provides an insight in their behavior, and in some interesting cases, tells us about the limiting behavior of the larger class of noisy channels.
Two classes of Very Noisy Channels are identified and efficient algorithms that compute their capacity are presented. We show that for some Very Noisy broadcast channels, the time-shared coding strategy performs as well as the optimal strategy known as broadcast coding in the limit. Finally, with the help of our model, we derive a tight lower bound on the amount of information lost in a Channel Reduction or Data Compression.
