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The best-known achievable rate region for the two-user Gaussian interference channel corresponds to the Han-Kobayashi scheme. However, mathematical expressions that characterize the Han-Kobayashi rate region are complicated. This complexity hinders a comprehensive understanding of the rate region. For instance, when interference is weak, the maximum achievable sum-rate of the Han-Kobayashi scheme has been unknown. This paper studies the sum-rate of the Han-Kobayashi scheme with Gaussian inputs and fully characterizes the maximum achievable sum-rate, when no time sharing is used. The optimal power-splitting variables and the corresponding maximum achievable sum-rate are explicitly expressed in closed forms. With the same approach, the maximum weighted sum-rate is expressed that characterizes the boundary of the Han-Kobayashi region without time sharing. Moreover, when time sharing is used, the boundary is expressed in terms of the upper concave envelope of a function of transmitters’ powers.

The generalized degrees of freedom (GDoF) region of the MIMO Gaussian interference channel (IC) is obtained for the general case of an arbitrary number of antennas at each node and where the signal-to-noise ratios (SNRs) and interference-to-noise ratios vary with arbitrary exponents to a nominal SNR. The GDoF-optimal coding scheme involves message splitting and partial interference decoding and consists of linear Gaussian superposition coding of the private and common submessages that can be seen as jointly performing signal-space and signal-level interference alignment. The admissible degree of freedom (DoF)-splits between the private and common messages are also specified. A study of the GDoF region reveals various insights through the joint dependence of optimal interference management techniques at high SNR on the SNR exponents and the numbers of antennas at the four terminals. For instance, it reveals that, unlike in the scalar IC, treating interference as noise is not always GDoF-optimal even in the very weak interference regime. Moreover, while the DoF-optimal strategy that relies just on transmit/receive zero-forcing beamforming and time sharing is not GDoF optimal (and thus has an unbounded gap to capacity), the precise characterization of the very strong interference regime-where single-user DoF performance can be achieved simultaneously for both users-depends on the relative numbers of antennas at the four terminals and thus deviates from what it is in the single-input single-output case. For asymmetric numbers of antennas at the four nodes, the shape of the symmetric GDoF curve can be a “distorted W” curve to the extent that for certain multiple-input multiple-output ICs it is a “V” curve.

In this paper, we focus on the general relay channel. We investigate the application of the estimate-and-forward (EAF) relaying scheme to different scenarios. Specifically, we study assignments of the auxiliary random variable that always satisfy the feasibility constraints. We then consider the Gaussian relay channel with coded modulation, where we show that a three-level quantization outperforms the Gaussian quantization commonly used to evaluate the achievable EAF rates in this scenario. Last, we consider the cooperative general broadcast scenario with a multistep conference between the receivers. We first apply EAF to obtain a general achievable rate region with a multistep conference. We then use an explicit assignment for the auxiliary random variables to obtain an explicit rate expression for the single common message case with a two-step conference.

The problem of separate zero-error coding of correlated sources is considered. Inner and outer single-letter bounds are established for the achievable rate region, and conditions for their coincidence are investigated. It is shown that successive encoding combined with time sharing is not always an optimal coding strategy. Conditions for its optimality are derived. The inner bound to the achievable rate region follows as a special case of the single-letter characterization of a generalized zero-error multiterminal rate-distortion problem. The applications of this characterization to a problem of remote computing are also explored. Other results include (i) a product-space characterization of the achievable rates, (ii) bounds for finite block length, and (iii) asymptotic fixed-length rates.

A discrete memoryless network (DMN) is a memoryless multiterminal channel with discrete inputs and outputs. A sequence of inner bounds to the DMN capacity region is derived by using code trees. Capacity expressions are given for three classes of DMNs: (1) a single-letter expression for a class with a common output, (2) a two-letter expression for a binary-symmetric broadcast channel (BC) with partial feedback, and (3) a finite-letter expression for push-to-talk DMNs. The first result is a consequence of a new capacity outer bound for common output DMNs. The third result demonstrates that the common practice of using a time-sharing random variable does not include all time-sharing possibilities, namely, time sharing of channels. Several techniques for improving the bounds are developed: (1) causally conditioned entropy and directed information simplify the inner bounds, (2) code trellises serve as simple code trees, (3) superposition coding and binning with code trees improves rates. Numerical computations show that the last technique enlarges the best known rate regions for a multiple-access channel (MAC) and a BC, both with feedback. In addition to the rate bounds, a sequence of inner bounds to the DMN reliability function is derived. A numerical example for a two-way channel illustrates the behavior of the error exponents.

Multiple description (MD) source coding is aimed at achieving graceful degradation in reconstruction with respect to losing portions of the code, with the cost of some redundancy. We examine MD schemes which use entropy-coded dithered lattice quantizers (ECDQ). We propose two techniques, one based on successive refinement (SR), and the other a dithered and periodic version of the MID scalar quantizer (MDSQ) with distributed cells proposed by Vaishampayan (1993, 1994). Similarly to the single description case, both techniques are universal in nature, and are equivalent to additive noise channels. This allows one to derive analytical expressions for the rate-distortion performance for general sources, and to compare them to the optimal rate regions at both high and low resolutions. Among other results, we establish that while the dithered MDSQ scheme loses only the space filling loss of the scalar lattice at any resolution, the SR-based scheme loses an additional 0.5 bit at any lattice dimension. Possible improvements, such as "refinement time sharing" and "dependent dithering", are discussed.

It is shown that the encoding/decoding problem for any asynchronous M-user memoryless multiple-access channel (MAC) can be reduced to corresponding problems for at most 2M-1 single-user memoryless channels. This is done via a method called generalized time sharing that is closely related to a previously developed method called rate-splitting multiple access. These methods reduce the seemingly hard task of finding good multiple-access codes and implementable decoders for such codes to the much better understood task of finding codes and decoders for single-user channels. As a by-product, some interesting properties of the capacity region of M-user asynchronous discrete memoryless channels are derived.

The achievable-rate region of sequential decoding for the class of pairwise reversible multiaccess channels is determined. This result is obtained by finding tight lower bounds to the average list size for the same class of channels. The average list size is defined as the expected number of incorrect messages that appear, to a maximum-likelihood decoder, to be at least as likely as the correct message. The average list size bounds developed here may be of independent interest, with possible applications to list-decoding schemes. © 1990 IEEE