Abstract. A code-division multiple-access system with channel coding may be viewed as a serially-concatenated coded system. In this paper we propose a low complexity method for decoding the resulting inner code (due to the spreading sequence), which allows iterative (turbo) decoding of the serially-concatenated code pair. The per-bit complexity of the proposed decoder increases only linearly with the number of users. Performance within a fraction of a dB of the single user bound for heavily loaded asynchronous CDMA is shown both by simulation and analytically.

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We consider multiple-input multiple-output (MIMO) transmit beamforming systems with maximum ratio combining (MRC) receivers. The operating environment is Rayleigh-fading with both transmit and receive spatial correlation. We present exact expressions for the probability density function (p.d.f.) of the output signal-to-noise ratio (SNR), as well as the system outage probability. The results are based on explicit closed-form expressions which we derive for the p.d.f. and c.d.f. of the maximum eigenvalue of double-correlated complex Wishart matrices. For systems with two antennas at either the transmitter or the receiver, we also derive exact closed-form expressions for the symbol error rate (SER). The new expressions are used to prove that MIMO-MRC achieves the maximum available spatial diversity order, and to demonstrate the effect of spatial correlation. The analysis is validated through comparison with Monte-Carlo simulations. 1 I. INTRODUCTION Multiple-input multiple-output (MIMO) antenna technology can provide significant improvements in capacity [1-4] and error performance [5] over conventional single-antenna technology, without requiring extra power or bandwidth. When channel knowledge is available at both the transmitter and receiver, MIMO transmit beamforming with maximum-ratio combining (MRC) receivers [6] is particularly robust against the severe effects of fading. This robustness is achieved by steering the transmitted signal along the maximum eigenmode of the MIMO channel, resulting in the maximization of the signal-to-noise ratio (SNR) at the MRC output. Recently, MIMO-MRC has been investigated in uncorrelated and semi-correlated channel scenarios (i.e. where correlation occurs at only one end of the transmission link, or not at all). A key to deriving analytical performance results is to statistically characterize the SNR at the output of the MRC combiner. In [7-11], uncorrelated Rayleigh fading was considered, and the output SNR statistical properties were derived based on maximum eigenvalue statistics of complex central Wishart matrices. In [12], uncorrelated Rician channels were characterized using maximum eigenvalue properties of complex noncentral Wishart matrices. Semi-correlated Rayleigh channels were considered in [13], utilizing properties of semi-correlated Wishart matrices. In this paper we consider double-correlated Rayleigh channels, by first deriving results for the eigenvalue statistics of double-correlated complex Wishart matrices. In practice, doublecorrelated channels (i.e. with correlation at both the transmitter and receiver) commonly occur due to, for example, insufficient scattering around both the transmit and receive terminals, or to closely spaced antennas with respect to the wavelength of the signal. While there are numerous statistical results on general Wishart matrices, there are almost no results for the eigenvalue statistics in the case of double-correlated Wishart matrices. In [14], the joint probability density function (p.d.f.) of the eigenvalues of such matrices wa...

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Information theoretic properties of flat fading channels with multiple antennas are investigated. Perfect channel knowledge at the receiver is assumed. Expressions for maximum information rates and outage probabilities are derived. The advantages of transmitter channel knowledge are determined and a critical threshold is found beyond which such channel knowledge gains very little. Asymptotic expressions for the error exponent are found. For the case of transmit diversity closed form expressions for the error exponent and cutoff rate are given. The use of orthogonal modulating signals is shown to be asymptotically optimal in terms of information rate.

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We present a new inner bound for the rate region of the t-stage successive-refinement problem with side-information. We also present a new upper bound for the rate-distortion function for lossysource coding with multiple decoders and side-information. Characterising this rate-distortion function is a long-standing open problem, and it is widely believed that the tightest upper bound is provided by Theorem 2 of Heegard and Berger's paper "Rate Distortion when Side Information may be Absent," IEEE Trans. Inform. Theory, 1985. We give a counterexample to Heegard and Berger's result. with side-information (fig. 4). A brief history of the literature on these problems is as follows. 1 Source q(x, y)Destination Fig. 1. The Wyner-Ziv Problem: (X, Y) = (X1, Y1), (X2, Y2), . . ., (Xn, Yn) is an iid random sequence emitted by a source q(x, y) = Pr[X = x, Y = y]. The encoder maps X to an index M , which belongs to a finite set M , at a rate r. Using M and Y, the decoder is required to generate a replicaX =X1,X2, . . . ,Xn of X to within an average distortion d, according to (1).The rate-distortion function R(d) is defined as the smallest rate for which such a reconstruction is possible. A single-letter expression for this function was first given in [1, Thm. 1].October 24, 2018 DRAFT A. The Wyner-Ziv Problem with t-DecodersSuppose that the side-information Y in Figure 1 is unreliable in the sense that it may or may not be available to the decoder. If the encoder does not know a priori when Y is available, thenWyner and Ziv's coding argument for (2) fails, and a more sophisticated argument is required to exploit Y. This observation inspired Kaspi [4] in 1980 (published by Wyner on behalf of Kaspi in 1994) as well as Heegard and Berger [5] in 1985 to independently study the problem shown in fig. 2 -the Kaspi/Heegard-Berger problem. As with the Wyner-Ziv problem, the objective of this problem is to characterise the corresponding rate-distortion function R (d 1 , d 2 ). That is, to find the smallest rate such that decoders 1 and 2 can produce replicasX 1 andX 2 of X to within average distortions d 1 and d 2 , respectively. To this end, Heegard and Berger [5, Thm. 1] showed that 1where the minimization is taken over all choices of two auxiliary random variables, U and W , that are jointly distributed with (X, Y ) and which satisfy the following two properties: (1) (U, W ) is conditionally independent of Y given X; and (2) there exist functionsX 1 (W ) and X 2 (Y, U, W ) with Eδ(X,X 1 (W )) ≤ d 1 and Eδ(X,X 2 (Y, U, W )) ≤ d 2 , respectively. The Kaspi/Heegard-Berger problem in Figure 2 was further generalised by Heegard and Berger in [5, Sec. VII] to the problem shown in Figure 3. There are t-decoders, each with different side-information, and the objective is to characterise the corresponding rate-distortion function R(d). Unfortunately, this function has eluded characterisation for all but a few special cases. For example, Heegard and Berger [5, Thm. 3] have characterised R(d) for stochastically degraded side-information 2 ;...