66 research outputs found
Randomly Spread CDMA: Asymptotics via Statistical Physics
This paper studies randomly spread code-division multiple access (CDMA) and
multiuser detection in the large-system limit using the replica method
developed in statistical physics. Arbitrary input distributions and flat fading
are considered. A generic multiuser detector in the form of the posterior mean
estimator is applied before single-user decoding. The generic detector can be
particularized to the matched filter, decorrelator, linear MMSE detector, the
jointly or the individually optimal detector, and others. It is found that the
detection output for each user, although in general asymptotically non-Gaussian
conditioned on the transmitted symbol, converges as the number of users go to
infinity to a deterministic function of a "hidden" Gaussian statistic
independent of the interferers. Thus the multiuser channel can be decoupled:
Each user experiences an equivalent single-user Gaussian channel, whose
signal-to-noise ratio suffers a degradation due to the multiple-access
interference. The uncoded error performance (e.g., symbol-error-rate) and the
mutual information can then be fully characterized using the degradation
factor, also known as the multiuser efficiency, which can be obtained by
solving a pair of coupled fixed-point equations identified in this paper. Based
on a general linear vector channel model, the results are also applicable to
MIMO channels such as in multiantenna systems.Comment: To be published in IEEE Transactions on Information Theor
One-Shot Mutual Covering Lemma and Marton's Inner Bound with a Common Message
By developing one-shot mutual covering lemmas, we derive a one-shot
achievability bound for broadcast with a common message which recovers Marton's
inner bound (with three auxiliary random variables) in the i.i.d.~case. The
encoder employed is deterministic. Relationship between the mutual covering
lemma and a new type of channel resolvability problem is discussed.Comment: 6 pages; extended version of ISIT pape
Mutual Information and Minimum Mean-square Error in Gaussian Channels
This paper deals with arbitrarily distributed finite-power input signals
observed through an additive Gaussian noise channel. It shows a new formula
that connects the input-output mutual information and the minimum mean-square
error (MMSE) achievable by optimal estimation of the input given the output.
That is, the derivative of the mutual information (nats) with respect to the
signal-to-noise ratio (SNR) is equal to half the MMSE, regardless of the input
statistics. This relationship holds for both scalar and vector signals, as well
as for discrete-time and continuous-time noncausal MMSE estimation. This
fundamental information-theoretic result has an unexpected consequence in
continuous-time nonlinear estimation: For any input signal with finite power,
the causal filtering MMSE achieved at SNR is equal to the average value of the
noncausal smoothing MMSE achieved with a channel whose signal-to-noise ratio is
chosen uniformly distributed between 0 and SNR
Support Recovery with Sparsely Sampled Free Random Matrices
Consider a Bernoulli-Gaussian complex -vector whose components are , with X_i \sim \Cc\Nc(0,\Pc_x) and binary mutually independent
and iid across . This random -sparse vector is multiplied by a square
random matrix \Um, and a randomly chosen subset, of average size , , of the resulting vector components is then observed in additive
Gaussian noise. We extend the scope of conventional noisy compressive sampling
models where \Um is typically %A16 the identity or a matrix with iid
components, to allow \Um satisfying a certain freeness condition. This class
of matrices encompasses Haar matrices and other unitarily invariant matrices.
We use the replica method and the decoupling principle of Guo and Verd\'u, as
well as a number of information theoretic bounds, to study the input-output
mutual information and the support recovery error rate in the limit of . We also extend the scope of the large deviation approach of Rangan,
Fletcher and Goyal and characterize the performance of a class of estimators
encompassing thresholded linear MMSE and relaxation
The Noncoherent Rician Fading Channel -- Part I : Structure of the Capacity-Achieving Input
Transmission of information over a discrete-time memoryless Rician fading
channel is considered where neither the receiver nor the transmitter knows the
fading coefficients. First the structure of the capacity-achieving input
signals is investigated when the input is constrained to have limited
peakedness by imposing either a fourth moment or a peak constraint. When the
input is subject to second and fourth moment limitations, it is shown that the
capacity-achieving input amplitude distribution is discrete with a finite
number of mass points in the low-power regime. A similar discrete structure for
the optimal amplitude is proven over the entire SNR range when there is only a
peak power constraint. The Rician fading with phase-noise channel model, where
there is phase uncertainty in the specular component, is analyzed. For this
model it is shown that, with only an average power constraint, the
capacity-achieving input amplitude is discrete with a finite number of levels.
For the classical average power limited Rician fading channel, it is proven
that the optimal input amplitude distribution has bounded support.Comment: To appear in the IEEE Transactions on Wireless Communication
The Noncoherent Rician Fading Channel -- Part II : Spectral Efficiency in the Low-Power Regime
Transmission of information over a discrete-time memoryless Rician fading
channel is considered where neither the receiver nor the transmitter knows the
fading coefficients. The spectral-efficiency/bit-energy tradeoff in the
low-power regime is examined when the input has limited peakedness. It is shown
that if a fourth moment input constraint is imposed or the input
peak-to-average power ratio is limited, then in contrast to the behavior
observed in average power limited channels, the minimum bit energy is not
always achieved at zero spectral efficiency. The low-power performance is also
characterized when there is a fixed peak limit that does not vary with the
average power. A new signaling scheme that overlays phase-shift keying on
on-off keying is proposed and shown to be optimally efficient in the low-power
regime.Comment: To appear in the IEEE Transactions on Wireless Communication
Relative entropy at the channel output of a capacity-achieving code
In this paper we establish a new inequality tying together the coding rate, the probability of error and the relative entropy between the channel and the auxiliary output distribution. This inequality is then used to show the strong converse, and to prove that the output distribution of a code must be close, in relative entropy, to the capacity achieving output distribution (for DMC and AWGN). One of the key tools in our analysis is the concentration of measure (isoperimetry).National Science Foundation (U.S.) (Grant CCF-06-35154)National Science Foundation (U.S.) (Grant CCF-07-28445
Scalar coherent fading channel: dispersion analysis
The backoff from capacity due to finite blocklength can be assessed accurately from the channel dispersion. This paper analyzes the dispersion of a single-user, scalar, coherent fading channel with additive Gaussian noise. We obtain a convenient two-term expression for the channel dispersion which shows that, unlike the capacity, it depends crucially on the dynamics of the fading process.National Science Foundation (U.S.) (Grant CCF-10-16625)National Science Foundation (U.S.) (CSol Grant Agreement CCF-09-39370
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