It is known that the Entropy Power Inequality (EPI) always holds if the random variables have density. Not much work has been done to identify discrete distributions for which the inequality holds with the differential entropy replaced by the discrete entropy. Harremoës and Vignat showed that it holds for the pair (B(m, p),B(n, p)), m, n ∈ ℕ, (where B(n, p) is a Binomial distribution with n trials each with success probability p) for p = 0.5. In this paper, we considerably expand the set of Binomial distributions for which the inequality holds and, in particular, identify n0(p) such that for all m, n ≥ n0(p), the EPI holds for (B(m, p),B(n, p)). We further show that the EPI holds for the discrete random variables that can be expressed as the sum of n independent and identically distributed (IID) discrete random variables for large n.

We study the fundamental properties of the quantum f-relative entropy, where f(·) is an operator convex function. We give the equality conditions under various properties including monotonicity and joint convexity, and these conditions apply to a class of operator convex functions that we define, and this class is different from the ones previously studied. The quantum f-entropy is defined in terms of the quantum f-relative entropy and we study its properties giving the equality conditions in some cases. We then show that the f-generalizations of the Holevo information, the entanglement-assisted capacity, and the coherent information also satisfy the data processing inequality, and give the equality conditions for the f-coherent information.

In this paper, we design capacity approaching low- density parity-check (LDPC) codes in the low signal-to-noise ratio (SNR) regime for flat Rayleigh fading channels with channel side information at transmitter and receiver. We use the structure advocated by Caire et al, which uses a single codebook with dynamic power allocation. The extrinsic information transfer (EXIT) function method is used to design the LDPC codes which approach the channel capacities. We also study the EXIT function properties of various demappers.

We study an improved receiver with iterative channel estimation and decoding for wireless multipath channels with RAKE reception. To keep the complexity low, iterative channel estimation is done on the equivalent channel at the RAKE output. Output after Turbo decoding iteration(s) is processed to yield a better channel estimate.

We construct a class of linear space-time block codes for any number of transmit antennas that have controllable ML decoding complexity with a maximum rate of 1 symbol per channel use. The decoding complexity for M transmit antennas can be varied from ML decoding of 2lceillog2Mrceil-1symbols together to single symbol ML decoding. For ML decoding of 2lceillog2Mrceil-n(n = 1,2,hellip) symbols together, a diversity of min(M, 2lceillog2Mrceil-n+1) can be achieved. Numerical results show that the performance of the constructed code when 2lceillog2Mrceil-1symbols are decoded together is quite close to the performance of ideal rate-1 orthogonal codes (that are non-existent for more than 2 transmit antennas).

Most classes of quasi-orthogonal space-time codes proposed in the literature require the use of rotated constellations for the interfering symbols to ensure full diversity. Since there is no analytical result available to get the exact probability of error in terms of the rotation angle, the optimization of the rotation angle has been done with respect to the Euclidean distance or the diversity product criteria. This paper provides analytical expressions for the optimal rotation angles for the Euclidean distance criteria for any M-PSK (phase shift keying) constellation.

We show that one can do away with the cyclic prefix (CP) for SC-FDE and OFDM at the cost of a moderate increase in complexity of a DFT-based receiver. Such an approach effectively deals with the decrease in the number of channel uses due to the introduction of the CP. It is shown that the SINR for SC-FDE remains the same asymptotically with the proposed receiver without CP as that of the conventional receiver with CP

It is shown that single symbol maximum-likelihood (ML) decoding for chosen rate 6/8 linear complex space-time codes for up to eight transmit antennas is possible in the presence of a phase feedback. The performance of the code is the same as that of an ideal code, for which the sufficient statistic of the channel is its Frobenius norm. For rate 1 codes for up to eight antennas, a two-phase feedback enables a symbol to see the interference from only one symbol instead of three, thereby reducing the complexity of ML decoding. Quantization of the feedback is also considered.

Recently proposed opportunistic beamforming exploits the multiuser diversity to reduce the feedback by not requiring the precoding information used for closed-loop schemes to be known at the transmitter. Opportunism could also be beneficially employed for other multiple-antenna transmission techniques like cophasing and antenna selection. For opportunistic beamforming and antenna selection, we give closed-form expressions for throughput that closely approximate the performance of these schemes with a Proportionally Fair scheduler (PFS) at low signal-to-noise ratios (SNRs). For large number of transmit antennas, opportunistic cophasing has similar performance as opportunistic beamforming. Asymptotic dependence of the required number of users to achieve the gains of opportunism on the number of transmit antennas is exponential for opportunistic beamforming (and cophasing for large numbers of transmit antennas), and at best linear for opportunistic antenna selection. For multiple-antenna receivers, we additionally examine an opportunistic multiple-input multiple-output (MIMO) scheme that transmits multiple data streams simultaneously to the same user.

The number of users that can be supported by frequency-hopped, spread-spectrum multiple-access systems can be increased greatly by using multiuser demodulation and iterative decoding. In the receiver employed hard-decision multiuser demodulation followed by iterative decoding, users exchange decoded information with each other. Additional information from multiuser demodulation in the first decoding iteration is limited by the hard-decision output of the multiuser demodulator. The error-correction used was an errors-and-erasures Reed-Solomon (RS) decoder. We revisit hard-decision demodulation and conventional RS decoding. Hard-decision multiuser demodulation is modified to provide a soft output, which is then given to a nonbinary block turbo code with shortened RS codes as the constituent codes. An iterative multiuser decoding algorithm is developed to do soft multiuser interference cancellation. This soft receiver with soft demodulation and decoding is shown to be more resistant to multiuser interference and channel noise, especially at lower values of signal-to-noise ratio. The results show a great improvement in the ability of the system to support more users (more than three times in some cases), as compared with systems that erase all hits or employ hard-decision multiuser demodulation followed by RS code. We examine the proposed method for synchronous as well as asynchronous frequency-hopped systems in both AWGN and fading channels.

In this letter, we show that the performance of recently proposed quasi-orthogonal space-time codes can be improved by phase-shifting the constellations of the symbols constituting the code. The optimal rotation of the symbols increases the minimum distance of the corresponding space-time codewords, leading to substantially improved performance.

Orthogonal codes are a class of space-time block codes that achieve full diversity gain, though typically at a loss of code rate. Such codes have simple single-symbol decoders. The code rate can be made higher by constructing quasi-orthogonal codes (such as those proposed last year in [1], [2]) which trade a small loss of performance for full rate coding. In this paper, which builds on previous work in [1], we propose a novel rotation technique for improving the performance of quasi-orthogonal codes in terms of bit-error rate (BER). Numerical simulations show that significant improvements to previously reported results without rotation can be attained.

Orthogonal codes are a class of space-time block codes that achieve full diversity, though at a loss of code rate. Such codes have simple single-symbol decoders. The code rate can be made higher by constructing quasi-orthogonal codes, which trade a small loss of performance for full rate coding. Typically, quasi-orthogonal codes perform the best when joint maximum likelihood (ML) decoding is used within subsets of the space-time codewords that are mutually orthogonal. We show that for a particular class of quasi-orthogonal codes, the interference which the subset of the symbols to be jointly decoded sees from other symbols is such that the signal to interference ratio remains constant for all channel realizations. Using the same constellation for all symbols in the subset reduces the minimum distance for such codes and results in a loss of performance. As a remedy to this problem, we introduce a rotation-based method that aims at maximizing the minimum distance in the space-time constellation. Numerical simulations show that significant improvements to previously reported results without rotation can be attained.

Demodulation and decoding for frequency-hopped spread-spectrum multiple-access (FH/SSMA) systems have been traditionally conducted by conventional single-user (noncollaborative) demodulation and error- and erasure-correcting decoding techniques. In this paper, we study the demodulation and decoding aspects of collaborative multiuser reception for FH/SSMA and propose methods which increase the number of users the system can support. In particular, we propose and analyze the optimum maximum a priori probability demodulation of multiple symbols or type, and the use of iterative multiuser decoding after the demodulation. Since hits from one or two other users are the most likely hit events in FH/SSMA, the joint demodulation of two or of three users is performed based on likelihood ratio tests. M-ary frequency-shift keying modulation with noncoherent demodulation and Reed-Solomon codes with hard-decision minimum distance decoding are used in the FH/SSMA system. Results are derived for both synchronous and asynchronous frequency-hop systems. The performance of the proposed multiuser detector in additive white Gaussian noise and flat Rayleigh fading channels is evaluated. Scenarios when all simultaneous users or only a subset of them are collaboratively demodulated and decoded are simulated.

Use of multiple antennas at the transmitter and the receiver to increase the information capacity has received considerable attention. To exploit the capability of such systems in a practical way, it is of interest to ask if there are good codes with reasonable decoding complexity. Another question of interest is the simplicity of design. This issue is particularly important in the case where the number of antennas in transmitter and receiver are large and a space-time code may be to complex to design and decode. We illustrate a class of codes which are simpler to design and the interference across antennas is suppressed by linear processing at the receiver. The performance of such codes is excellent and much better than the group interference suppression techniques employed in conjunction with the space-time codes. Use of error detection schemes is shown to further improve the performance without much change in the design of codes and decoding complexity.

It has been shown that the capacity of a slow frequency hopped (SFH) spread spectrum multiple access (SSMA) system can be increased by using the joint demodulation and iterative decoding by a hard decision demodulator with Reed Solomon code as a forward error correcting code. In this paper, we revisited the FSK demodulation and the conventional RS decoding. The FSK demodulation was modified to do joint demodulation and provide the soft decision of the type in the presence of multi-user interference. The conventional RS decoding was replaced by a block turbo code consisting of two shortened RS codes with interleaving between them. An iterative multi-user decoding algorithm is developed to do a soft collaborative decoding. This 'soft core' of the decoder is shown to be more resistant to the multi-user interference and the channel noise. The results show a great improvement in the capacity of the system as compared to systems which erase the hits or which employ hard decision in the joint demodulation.

Multiuser detection for frequency hop spread spectrum multiple access (FH/SSMA) systems has been traditionally done by conventional single user decoding or by erasure techniques. We study the demodulation and decoding aspects of multiuser reception for SFH/SSMA and propose methods which improve the capacity of the system. In particular, we propose and analyze the joint demodulation of multiple symbols and the use of iterative decoding after the demodulation. For the hard decision demodulation, need Solomon codes of different users collaborate with each other after the joint demodulation to reduce the multi-user interference. This approach is then extended for the soft decision demodulation and decoding where a block turbo code consisting of two shortened RS codes is employed. Results are shown both for synchronous and asynchronous frequency hop systems and indicate considerable improvement over the conventional systems.

The theory of space-time codes for multiple antennas at the transmitter and receiver provided a useful framework for minimizing the probability of pair-wise frame error when the channel is unknown at the receiver. The design criterion for the codes were developed by averaging over all the channel states. In practice, a feedback channel of low bandwidth is usually available where the transmitter can get some channel state information from the receiver. The transmitter can use this information to change its power level or modulation or both. Since the channel state is a matrix instead of a scalar in the single antenna case, we first find out what is the sufficient statistic for space-time orthogonal block codes. It is shown that for a given channel state, the decoder essentially sees an AWGN channel with the signal to noise ratio scaled by the sufficient statistic. We discuss the optimal power control and adaptive modulation strategies. The effect of delay in passing the channel information from the receiver to the transmitter is examined. The results show a significant improvement (more than 10 dB in some cases) over the conventional system without feedback.

There have been various proposals for communication with chaotic signals. But the issue of compensating the distortions introduced by the physical channel like noise, time varying fading and multi-path has not been fully addressed. In this paper, we first describe a noise reduction method for chaotic signals corrupted by additive noise. The method uses the phenomenon of chaos synchronization to approximate the maximum likelihood (ML) decoder for the AWGN channel. Further we use a synchronizing receiver to nullify slowly time varying fading and multi-path. We find the region of operation for such a receiver and show how the time varying parameters characterizing such channels can be tracked at the receiver.