Coding schemes for several problems in network information theory are constructed starting from point-to-point channel codes that are designed for symmetric channels. Given that the point-to-point codes satisfy certain properties pertaining to the rate, the error probability, and the distribution of decoded sequences, bounds on the performance of the coding schemes are derived and shown to hold irrespective of other properties of the codes. In particular, we consider the problems of lossless and lossy source coding, Slepian–Wolf coding, Wyner–Ziv coding, Berger–Tung coding, multiple description coding, asymmetric channel coding, Gelfand–Pinsker coding, coding for multiple access channels, Marton coding for broadcast channels, and coding for cloud radio access networks (C-RAN’s). We show that the coding schemes can achieve the best known inner bounds for these problems, provided that the constituent point-to-point channel codes are rate-optimal. This would allow one to leverage commercial off-the-shelf codes for point-to-point symmetric channels in the practical implementation of codes over networks. Simulation results demonstrate the gain of the proposed coding schemes compared to existing practical solutions to these problems.

A new approach to$L_{2}$-consistent estimation of a general density functional using$k$-nearest neighbor distances is proposed, where the functional under consideration is in the form of the expectation of some function$f$of the densities at each point. The estimator is designed to be asymptotically unbiased, using the convergence of the normalized volume of a$k$-nearest neighbor ball to a Gamma distribution in the large-sample limit, and naturally involves the inverse Laplace transform of a scaled version of the function$f$. Some instantiations of the proposed estimator recover existing$k$-nearest neighbor based estimators of Shannon and Rényi entropies and Kullback–Leibler and Rényi divergences, and discover new consistent estimators for many other functionals such as logarithmic entropies and divergences. The$L_{2}$-consistency of the proposed estimator is established for a broad class of densities for general functionals, and the convergence rate in mean squared error is established as a function of the sample size for smooth, bounded densities.

Coding schemes for asymmetric channels and channels with state are developed starting from a pair of linear codes designed for symmetric channels. Guarantees on the block error rate performance of the coding schemes are derived in terms of the parameters of the constituent codes. Assuming the constituent codes satisfy some properties on the rate, the error probability, and the distribution of the Hamming distance to decoded sequences, the performance guarantees hold irrespective of other properties of the codes. This would allow one to leverage commercial off-the-shelf codes for point-to-point symmetric channels to design codes for asymmetric channels and channels with state known noncausally at the encoder.

Uplink and downlink cloud radio access networks are modeled as two-hop K-user L-relay networks, whereby small base-stations act as relays for end-to-end communications and are connected to a central processor via orthogonal fronthaul links of finite capacities. Simplified versions of network compress-forward (or noisy network coding) and distributed decode-forward are presented to establish inner bounds on the capacity region for uplink and downlink communications, that match the respective cutset bounds to within a finite gap independent of the channel gains and signal to noise ratios. These approximate capacity regions are then compared with the capacity regions for networks with no capacity limit on the fronthaul. Although it takes infinite fronthaul link capacities to achieve these “fronthaul-unlimited” capacity regions exactly, these capacity regions can be approached approximately with finite-capacity fronthaul. The total fronthaul link capacities required to approach the fronthaul-unlimited sum-rates (for uplink and downlink) are characterized. Based on these results, the capacity scaling law in the large network size limit is established under certain uplink and downlink network models, both theoretically and via simulations.

Codes are developed for two-user multiple access and broadcast channels starting from Gelfand-Pinsker codes with known block lengths, rates, and error performances. Guarantees are provided on the block error rates of the MAC and BC codes in terms of the parameters of the constituent Gelfand- Pinsker codes. These guarantees hold as long as the constituent codes satisfy the assumed properties on rate, codeword weights, and performances, irrespective of the basic structure and other properties.

A low-complexity coding scheme, termed as sliding-window Gelfand–Pinsker coding, is proposed. It is shown that in a general K-user broadcast channel, every rate point in the Marton’s inner bound can be achieved using single-user encoders and decoders. The scheme provides us with a low-complexity alternative to implement the conceptual K dimensional multi-coding, which is an irreplaceable component in many important network communication schemes, such as Marton coding in Gaussian MIMO broadcast channels and distributed decode–forward in cloud radio access networks, but has not been adopted in practical systems due to high computational complexity. Key features in the proposed scheme include staggered message scheduling, successive Gelfand–Pinsker coding, and sliding-window decoding.

Uplink and downlink cloud radio access networks are modeled as two-hop K-user L-relay networks, whereby small base-stations act as relays and are connected to a central processor via orthogonal fronthaul links of finite capacities. Based on noisy network coding and distributed decode-forward inner bounds on the capacity regions for uplink and downlink, respectively, the total fronthaul link capacity required to approach the centralized MIMO sum-rate is characterized. The capacity scaling law when the network size increases is examined under certain uplink and downlink network models, both theoretically and via simulations.

Uplink and downlink cloud radio access networks are modeled as two-hop K-user L-relay networks, whereby small base-stations act as relays and are connected to a central processor via orthogonal links of finite capacity. Simplified versions of noisy network coding and distributed decode-forward are used to establish inner bounds on the capacity region for uplink and downlink communications, respectively. Through a careful analysis, the uplink inner bound is shown to achieve the cutset bound on the capacity region universally within O (log L) bits per user. The downlink inner bound achieves the cutset bound with a slightly looser gap of O(log(KL)). These tight per-user gap results are extended to the situations in which the nodes have multiple antennas.

We consider non parametric sequential hypothesis testing problem when the distribution under the null hypothesis is fully known but the alternate hypothesis corresponds to some other unknown distribution with some loose constraints. We propose a simple algorithm to address the problem. This is also generalized to the case when the distribution under the null hypothesis is not fully known. These problems are primarily motivated from wireless sensor networks and spectrum sensing in Cognitive Radios. A decentralized version utilizing spatial diversity is also proposed. Its performance is analysed and asymptotic properties are proved. The simulated and analysed performance of the algorithm are shown to be better than an earlier algorithm addressing the same problem with similar assumptions. We also modify the algorithm for optimizing performance when information about the prior probabilities of occurrence of the two hypotheses are known.