Youjian Liu

On the design of MIMO block-fading channels with feedback-link capacity constraint

In this paper, we propose a combined adaptive power control and beamforming framework for optimizing multiple-input/multiple-output (MIMO) link capacity in the presence of feedback-link capacity constraint. The feedback channel is used to carry channel state information only. It is assumed to be noiseless and causal with a feedback capacity constraint in terms of maximum number of feedback bits per fading block. We show that the hybrid design could achieve the optimal MIMO link capacity, and we derive a computationally efficient algorithm to search for the optimal design under a specific average power constraint. Finally, we shall illustrate that a minimum mean-square error spatial processor with a successive interference canceller at the receiver could be used to realize the optimal capacity. We found that feedback effectively enhances the forward channel capacity for all signal-to-noise ratio (SNR) values when the number of transmit antennas (n/sub T/) is larger than the number of receive antennas (n/sub R/). The SNR gain with feedback is contributed by focusing transmission power on active eigenchannel and temporal power waterfilling . The former factor contributed, at most, 10log/sub 10/(n/sub T//n/sub R/) dB SNR gain when n/sub T/>n/sub R/, while the latter factors SNR gain is significant only for low SNR values.

Quantization Bounds on Grassmann Manifolds and Applications to MIMO Communications

The Grassmann manifold Gn,p (L) is the set of all p-dimensional planes (through the origin) in the n-dimensional Euclidean space Ln, where L is either R or C. This paper considers the quantization problem in which a source in Gn,p (L) is quantized through a code in Gn,q (L), with p and q not necessarily the same. The analysis is based on the volume of a metric ball in Gn,p (L) with center in Gn,q (L), and our chief result is a closed-form expression for the volume of a metric ball of radius at most one. This volume formula holds for arbitrary n, p, q, and L, while previous results pertained only to some special cases. Based on this volume formula, several bounds are derived for the rate-distortion tradeoff assuming that the quantization rate is sufficiently high. The lower and upper bounds on the distortion rate function are asymptotically identical, and therefore precisely quantify the asymptotic rate-distortion tradeoff. We also show that random codes are asymptotically optimal in the sense that they achieve the minimum possible distortion in probability as n and the code rate approach infinity linearly. Finally, as an application of the derived results to communication theory, we quantify the effect of beamforming matrix selection in multiple-antenna communication systems with finite rate channel state feedback.

Full rate space-time turbo codes

This paper proposes a class of full space diversity full rate space-time turbo codes. Both parallel concatenated and serially concatenated codes are designed. A rank theory proposed by the authors earlier is employed to check the full space diversity of the codes. The simulations show that the space-time turbo codes can take full advantage of space diversity and time diversity if they are available in the channels. We also study the robustness of performance of both turbo codes and trellis codes in space-time correlated fading channels.

High-Throughput Layered LDPC Decoding Architecture

This paper presents a high-throughput decoder architecture for generic quasi-cyclic low-density parity-check (QC-LDPC) codes. Various optimizations are employed to increase the clock speed. A row permutation scheme is proposed to significantly simplify the implementation of the shuffle network in LDPC decoder. An approximate layered decoding approach is explored to reduce the critical path of the layered LDPC decoder. The computation core is further optimized to reduce the computation delay. It is estimated that 4.7 Gb/s decoding throughput can be achieved at 15 iterations using the current technology.

On the design of space-time and space-frequency codes for MIMO frequency-selective fading channels

The authors introduced an algebraic design framework for space-time coding in flat-fading channels . We extend this framework to design algebraic codes for multiple-input multiple-output (MIMO) frequency-selective fading channels. The proposed codes strive to optimally exploit both the spatial and frequency diversity available in the channel. We consider two design approaches: The first uses space-time coding and maximum likelihood decoding to exploit the multi-path nature of the channel at the expense of increased receiver complexity. Within this time domain framework, we also propose a serially concatenated coding construction which is shown to offer a performance gain with a reasonable complexity iterative receiver in some scenarios. The second approach utilizes the orthogonal frequency division multiplexing technique to transform the MIMO multipath channel into a MIMO flat block fading channel. The algebraic framework is then used to construct space-frequency codes (SFC) that optimally exploit the diversity available in the resulting flat block fading channel. Finally, the two approaches are compared in terms of decoder complexity, maximum achievable diversity advantage, and simulated frame error rate performance in certain representative scenarios.

Optimal rate allocation for superposition coding in quasi-static fading channels

Coding with a single fixed rate may not achieve the maximum throughput of a compound channel if the transmitter only has access to channel state statistics. Superposition coding for broadcast channels can be employed to increase the throughput. We study the optimal rate allocation for finite level superposition coding to maximize the throughput. Results show 2-level superposition coding is adequate to achieve most of the throughput gain in a quasi-static Rayleigh fading channel.

Space-time codes performance criteria and design for frequency selective fading channels

This paper studies the space time code design for single carrier transmission over frequency selective fading channels. The design criteria are derived first and then we apply the algebraic /spl Sigma//sub 0/-rank theory to show how to design codes to take advantage of space and frequency diversity simultaneously. Finally, example codes are shown to achieve desired level of diversity by simulation results.

Capacity of memoryless channels and block-fading channels with designable cardinality-constrained channel state feedback

A coding theorem is proved for memoryless channels when the channel state feedback of finite cardinality can be designed. Channel state information is estimated at the receiver and a function of the estimated channel state is causally fed back to the transmitter. The feedback link is assumed to be noiseless with a finite feedback alphabet, or equivalently, finite feedback rate. It is shown that the capacity can be achieved with a memoryless deterministic feedback and with a memoryless device which select transmitted symbols from a codeword of expanded alphabet according to current feedback. To characterize the capacity, we investigate the optimization of transmission and channel state feedback strategies. The optimization is performed for both channel capacity and error exponents. We show that the design of the optimal feedback scheme is identical to the design of scalar quantizer with modified distortion measures. We illustrate the optimization using Rayleigh block-fading channels. It is shown that the optimal transmission strategy has a general form of temporal water-filling in important cases. Furthermore, while feedback enhances the forward channel capacity more effectively in low-signal-to noise ratio (SNR) region compared with that of high-SNR region, the enhancement in error exponent is significant in both high- and low-SNR regions. This indicates that significant gain due to finite-rate channel state feedback is expected in practical systems in both SNR regions.

On the Information Rate of MIMO Systems With Finite Rate Channel State Feedback Using Beamforming and Power On/Off Strategy

It is well known that multiple-input multiple-output (MIMO) systems have high spectral efficiency, especially when channel state information at the transmitter (CSIT) is available. In many practical systems, it is reasonable to assume that the CSIT is obtained by a limited (i.e., finite rate) feedback and is therefore imperfect. We consider the design problem of how to use the limited feedback resource to maximize the achievable information rate. In particular, we develop a low complexity power on/off strategy with beamforming (or Grassmann precoding), and analytically characterize its performance. Given the eigenvalue decomposition of the covariance matrix of the transmitted signal, refer to the eigenvectors as beams, and to the corresponding eigenvalues as the beams power. A power on/off strategy means that a beam is either turned on with a constant power, or turned off. We will first assume that the beams match the channel perfectly and show that the ratio between the optimal number of beams turned on and the number of antennas converges to a constant when the numbers of transmit and receive antennas approach infinity proportionally. This motivates our power on/off strategy where the number of beams turned on is independent of channel realizations but is a function of the signal-to-noise ratio (SNR). When the feedback rate is finite, beamforming cannot be perfect, and we characterize the effect of imperfect beamforming by quantization bounds on the Grassmann manifold. By combining the results for power on/off and beamforming, a good approximation to the achievable information rate is derived. Simulations show that the proposed strategy is near optimal and the performance approximation is accurate for all experimented SNRs.

A Low Complexity Protocol for Relay Channels Employing Rateless Codes and Acknowledgement

We provide a low complexity communication protocol for relay channels that can achieve a significant rate reliably even when a code word spans only finite number of fading blocks on average. Both full duplex and half duplex relay are considered. In the past, when a fixed rate code word spans a finite number of fading blocks, the capacity is zero. Therefore, a large amount of research has tried to reduce outage probability and increase throughput, such as the high signal-to-noise ratio (SNR) diversity-and-multiplexing-gain-tradeoff study of relay channels. Differently, the protocol in this paper achieves a significant information rate with asymptotically zero error probability (no outage) when the number of information bits represented by a code word increases to infinity. This performance is achieved by employing rateless codes and acknowledgements so that the destination obtains just enough mutual information to decode. This approach has the advantages that the protocol is not channel statistics dependent, has low complexity, is power efficient, has high performance, and can be easily generalized to other network communication settings