Information Networks with in-Block Memory

A class of channels is introduced for which there is memory inside blocks of a specified length and no memory across the blocks. The multi-user model is called an information network with in-block memory (NiBM). It is shown that block-fading channels, channels with state known causally at the encoder, and relay networks with delays are NiBMs. A cut-set bound is developed for NiBMs that unifies, strengthens, and generalizes existing cut bounds for discrete memoryless networks. The bound gives new finite-letter capacity expressions for several classes of networks including point-to-point channels, and certain multiaccess, broadcast, and relay channels. Cardinality bounds on the random coding alphabets are developed that improve on existing bounds for channels with action-dependent state available causally at the encoder and for relays without delay. Finally, quantize-forward network coding is shown to achieve rates within an additive gap of the new cut-set bound for linear, additive, Gaussian noise channels, symmetric power constraints, and a multicast session.