Outer bounds on the capacity of Gaussian interference channels

Two outer bounds on the capacity region of the two-user Gaussian interference channel (IFC) are derived. The idea of the first bound is to let a genie give each receiver just enough information to decode both messages. This bound unifies and improves the best known outer bounds of Sato and Carleial. Furthermore, the bound extends to discrete memoryless IFCs and is shown to be equivalent to another bound of Carleial. The second bound follows directly from existing results of Costa and Sato and possesses certain optimality properties for weak interference.     

Linear feedback rate bounds for regressive channels (Corresp.)

This article presents new tighter upper bounds on the rate of Gaussian autoregressive channels with linear feedback. The separation between the upper and lower bounds is small. We havefrac{1}{2} ln left( 1 + rho left( 1+ sum_{k=1}^{m} alpha_{k} x^{- k} right)^{2} right) leq C_{L} leq frac{1}{2} ln left( 1+ rho left( 1+ sum_{k = 1}^{m} alpha_{k} / sqrt{1 + rho} right)^{2} right), mbox{all rho}, whererho = P/N_{0}W, alpha_{l}, cdots, alpha_{m}are regression coefficients,Pis power,Wis bandwidth,N_{0}is the one-sided innovation spectrum, andxis a root of the polynomial(X^{2} - 1)x^{2m} - rho left( x^{m} + sum^{m}_{k=1} alpha_{k} x^{m - k} right)^{2} = 0.It is conjectured that the lower bound is the feedback capacity.     

The capacity region of a class of discrete additive degraded interference channels (Corresp.)

A single-letter characterization of the capacity region for a class of discrete degraded interference channels (IFC's) is determined. This class of degraded IFC's has an additive structure similar to that of a class of degraded Gaussian IFC's. The capacity region for this class of degraded IFC's is shown to be also the capacity region of a related class of degraded broadcast channels (DBC's). The singie-letter characterization obtained for this region simplifies the computation of the capacity region of this related class of DBC's.     

The capacity of the Gaussian interference channel under strong interference (Corresp.)

The capacity region of a Gaussian interference channel with two separate messages is obtained for the case of moderately strong interference. It is shown that the region coincides with the one where both messages are required in both receiving terminals.     

The coding capacity of mismatched Gaussian channels (Corresp.)

Bounds on the coding capacity of Gaussian channels are obtained when the power constraint on the signal is mismatched to the channel noise. In the case of some feedback channels in which the noise has a Cramér-Hida representation of finite multiplicity, an exact expression for the coding capacity is given.     

The feedback capacity of degraded broadcast channels (Corresp.)

The fact that the capacity region of the discrete memoryless physically degraded broadcast channel is not increased by feedback is established.     

The capacity region of the discrete memoryless interference channel with strong interference (Corresp.)

The capacity region of the discrete memoryless interference channel with strong interference is established.     

A case where interference does not reduce capacity (Corresp.)

It is shown that, under certain conditions, two strongly interfering communication links with additive white Gaussian noise can achieve rates as high as would be achievable without this interference.     

Modified Chernoff bounds for PAM systems with noise and interference (Corresp.)

By using principles of analytic continuation, upper and lower bounds on the error probability of a canonical binary system corrupted by additive interference and independent zero-mean Gaussian noise are derived. The bounds, which are simple functions, require only the evaluation or bounding of the moment generating function of the interference. For large signal-to-noise ratios (SNR) and even for moderately large interference, the bounds are shown to be tight and useful.     

A note on lower bounds (Corresp.)

A new lower bound for the parameters of (nonlinear)q-ary codes is introduced. For some q this bound improves on the Varshamov-Gilbert bound, the "modular" algebraic-geometric bound, and the very recent Vlbreve{a}duts bound.     

On the capacity of a class of mismatched Gaussian channels (Corresp.)

The capacity is considered for Gaussian channels where the channel noise covariance is not the same as the constraint covariance. An upper bound is obtained; sharper results are obtained under additional assumptions.     

Power spectral density bounds (Corresp.)

The determination of a power density spectrum from a finite set of correlation samples is an ill-posed problem. Furthermore. it is not possible even to bound the values that consistent power density spectra can take on at a particular point. A more reasonable problem is to try to determine the total spectral power in some frequency interval. Although this power cannot be determined exactly, upper and lower bounds on its possible values can be determined. This observation leads to a unified treatment of certain classical and modern spectral estimation techniques and to new interpretations for two data adaptive spectral estimators. maximum likelihood method (MLM) and data adaptive spectral estimator (DASE). According to these new interpretations. MLM and DASE provide upper bounds on spectral power in a specified frequency region subject to the assumption that the spectral density is constant in that region. These methods make no use of an extendibility constraint that can be used to obtain tight upper bounds, as well as nontrivial lower bounds on power. Cybenko has studied a related problem of bounding windowed power, for an arbitrary window, with no assumptions about the form of the spectral density. A new type of classical resolution limit for these bounds is derived and a numerical example is presented.     

An outer bound to the capacity region of broadcast channels (Corresp.)

An outer bound to the capacity region of broadcast channels for the transmission of separate messages is derived. This bound improves upon Cover's outer bound by taking into consideration the total throughput information rate and the fact that the capacity region depends only on the marginal transition probabilities.     

Upper bounds on codes correcting asymmetric errors (Corresp.)

A Survey is given of known upper bounds on codes correcting asymmetric errors. The bounds are improved by introducing new Ideas. By solving a linear programming problem an upper bound is given that is easy to compute for all codelengths and all minimum asymmetric distances.     

On the capacity region of a discrete two-user channel for strong interference (Corresp.)

The capacity region of a simple discrete two-user channel for the transmission of two separate messages is studied in the strong interference case. It is shown that in this case the inner bound to the capacity region practically coincides with the outer bound.     

On the capacity of a cascade of identical discrete memoryless nonsingular channels (Corresp.)

A simplified procedure for calculating the channel capacity of a cascade ofNidentical discrete memoryless nonsingular channels is presented. The result depends only upon theMeigenvalues andMeigenvectors of any one of the subchannel transition matrices. Thus, for smallMand largeN(the usual case of interest) the result represents a considerable saving in computation relative to the standard technique of finding the overall channel transition matrix. The procedure is illustrated for anNcascade of binary symmetric channels.     

Two-user dispersive communication channels (Corresp.)

The optimum transmitters for maximum information throughput when two independent users share a dispersive channel are investigated. The channel is assumed to be linear and time invariant and is described by a2 times 2matrix of transfer functions. The noise at each receiver is additive and Gaussian and may have a nonwhite spectrum. Assuming naive superposition (the interfering signal is treated as noise) it is shown that for many practical channels, frequency division multiplexing is optimum, and the structure of the optimum transmitters is obtained.     

Lower bounds on the maximum cross correlation of signals (Corresp.)

Some communication systems require sets of signals with impulse-like autocorrelation functions and small cross correlation. There is considerable literature on signals with impulse-like autocorrelation functions hut little on sets of signals with small cross correlation. A possible reason is that designers put too severe a restriction on cross correlation magnitudes. This correspondence establishes lower bounds on how small the cross correlation and autocorrelation can simultaneously be.     

Linear programming bounds for tree codes (Corresp.)

Two asymptotic upper bounds on the information rate of a tree code as a function of its feedback decoding minimum distance are presented. These bounds are generalizations of the linear programming bounds for binary block codes proved by McEliece et al., and they are derived from linear programming problems based on Delsarte's theory of association schemes.