These lecture notes have been converted to a book titled Network Information Theory published recently by Cambridge University Press. This book provides a significantly expanded exposition of the material in the lecture notes as well as problems and bibliographic notes at the end of each chapter. The authors are currently preparing a set of slides based on the book that will be posted in the second half of 2012.More information about the book can be found at

A relay channel consists of an input x,, a relay output yl, a cJmnnel output y, and a relay sender x2 (whose trasmission is allowed to depend on the past symbols y,). l%e dependence of the received symbols upm the inpnts is given by p(y,y,lx,,x,). 'l%e channel is assumed to be memoryless. In this paper the following capacity theorems are proved.

Via Ca 2+ -imaging in freely behaving mice that repeatedly explored a familiar environment, we tracked thousands of CA1 pyramidal cells' place fields over weeks. Place coding was dynamic, for each day the ensemble representation of this environment involved a unique subset of cells. Yet, cells within the ∼15-25% overlap between any two of these subsets retained the same place fields, which sufficed to preserve an accurate spatial representation across weeks.CA1 place cells are considered crucial for spatial memory, but data is limited regarding whether their representations of space evolve over time scales of weeks or more 1 . Some theories suggest place cells should retain stable place fields for long-term retention of familiar environments 1 . Alternatively, dynamic aspects of place coding may facilitate distinct memory traces of different events occurring in the same environment 2 .Due to technical limitations, it has been only partially explored if CA1 representations of familiar environments are stable or evolve over time. Electrical recordings from many tens of cells are feasible 3 , but it is challenging to record from the same cells longer than a few days. Data on place fields' stability has largely been from small numbers of cells recorded over at most a week [4][5][6][7][8][9][10] . These studies have demonstrated cells with stable place fields, but the data have been too sparse to assess how coding evolves at the ensemble level.To study long-term coding dynamics, we combined (Fig. 1a): a viral vector (AAV2/5-CamKIIα-GCaMP3) to express the Ca 2+ -indicator GCaMP3 11 in pyramidal cells; a chronic mouse preparation for time-lapse imaging of CA1 over weeks 12 ; and a miniaturized (<2 g) microscope for Ca 2+ -imaging in hundreds of cells in freely behaving mice 13 . We thereby tracked somatic Ca 2+ dynamics of 515-1040 pyramidal cells in individual mice as they repeatedly visited a familiar track over 45 days.

The light microscope is traditionally an instrument of substantial size and expense. Its miniaturized integration would enable many new applications based on mass-producible, tiny microscopes. Key prospective usages include brain imaging in behaving animals towards relating cellular dynamics to animal behavior. Here we introduce a miniature (1.9 g) integrated fluorescence microscope made from mass-producible parts, including semiconductor light source and sensor. This device enables high-speed cellular-level imaging across ∼0.5 mm2 areas in active mice. This capability allowed concurrent tracking of Ca2+ spiking in >200 Purkinje neurons across nine cerebellar microzones. During mouse locomotion, individual microzones exhibited large-scale, synchronized Ca2+ spiking. This is a mesoscopic neural dynamic missed by prior techniques for studying the brain at other length scales. Overall, the integrated microscope is a potentially transformative technology that permits distribution to many animals and enables diverse usages, such as portable diagnostics or microscope arrays for large-scale screens.

A new coding scheme for multicasting multiple sources over a general noisy network is presented. The scheme naturally extends both network coding over noiseless networks by Ahlswede, Cai, Li, and Yeung, and compress-forward coding for the relay channel by Cover-EI Gamal to general discrete memoryless and Gaussian networks. The scheme also recovers as special cases the results on coding for wireless relay networks and deterministic networks by Avestimehr, Diggavi, and Tse, and coding for wireless erasure networks by Dana, Gowaikar, Palanki, Hassibi, and Effros. The key idea is to use block Markov message repetition coding and simultaneous decoding. Instead of sending multiple independent messages over several blocks and decoding them sequentially as in previous relaying schemes, the same mes sage is sent multiple times using independent codebooks and the decoder performs joint typicality decoding on the received signals from all the blocks without explicitly decoding the compression indices. New results on semideterministic relay networks and Gaussian networks demonstrate the potential of noisy network coding as a robust and scalable scheme for communication over wireless networks.