Optimization of Joint Progressive Source and Channel Coding for MIMO Systems

The optimization of joint source and channel coding for a sequence of numerous progressive packets is a challenging problem. Further, the problem becomes more complicated if the space- time coding is also involved with the optimization in a multiple-input multiple-output (MIMO) system. This is because the number of ways of jointly assigning channel codes and space-time codes to progressive packets is much larger than that of solely assigning channel codes to the packets. This paper applies a parametric approach to address that complex joint optimization problem in a MIMO system. Employing the parametric distortion-rate function, the joint assignment of channel codes and space-time codes to the packets can be optimized in a packet-by- packet manner. As a result, the computational complexity of the optimization is exponentially reduced, compared to the exhaustive search. The numerical results show that the proposed method significantly improves the peak-signal-to-noise ratio performance of the rate-based optimal solution in a MIMO system

Distortion Exponent in MIMO Fading Channels with Time-Varying Source Side Information

Transmission of a Gaussian source over a time-varying multiple-input multiple-output (MIMO) channel is studied under strict delay constraints. Availability of a correlated side information at the receiver is assumed, whose quality, i.e., correlation with the source signal, also varies over time. A block-fading model is considered for the states of the time-varying channel and the time-varying side information; and perfect state information at the receiver is assumed, while the transmitter knows only the statistics. The high SNR performance, characterized by the \textit{distortion exponent}, is studied for this joint source-channel coding problem. An upper bound is derived and compared with lowers based on list decoding, hybrid digital-analog transmission, as well as multi-layer schemes which transmit successive refinements of the source, relying on progressive and superposed transmission with list decoding. The optimal distortion exponent is characterized for the single-input multiple-output (SIMO) and multiple-input single-output (MISO) scenarios by showing that the distortion exponent achieved by multi-layer superpositon encoding with joint decoding meets the proposed upper bound. In the MIMO scenario, the optimal distortion exponent is characterized in the low bandwidth ratio regime, and it is shown that the multi-layer superposition encoding performs very close to the upper bound in the high bandwidth expansion regime.Comment: Submitted to IEEE Transactions on Information Theor

Distortion Exponent in MIMO Channels with Feedback

The transmission of a Gaussian source over a block-fading multiple antenna channel in the presence of a feedback link is considered. The feedback link is assumed to be an error and delay free link of capacity 1 bit per channel use. Under the short-term power constraint, the optimal exponential behavior of the end-to-end average distortion is characterized for all source-channel bandwidth ratios. It is shown that the optimal transmission strategy is successive refinement source coding followed by progressive transmission over the channel, in which the channel block is allocated dynamically among the layers based on the channel state using the feedback link as an instantaneous automatic repeat request (ARQ) signal.Comment: Presented at the IEEE Information Theory Workshop (ITW), Taormina, Italy, Oct. 200

Distortion Minimization in Gaussian Layered Broadcast Coding with Successive Refinement

A transmitter without channel state information (CSI) wishes to send a delay-limited Gaussian source over a slowly fading channel. The source is coded in superimposed layers, with each layer successively refining the description in the previous one. The receiver decodes the layers that are supported by the channel realization and reconstructs the source up to a distortion. The expected distortion is minimized by optimally allocating the transmit power among the source layers. For two source layers, the allocation is optimal when power is first assigned to the higher layer up to a power ceiling that depends only on the channel fading distribution; all remaining power, if any, is allocated to the lower layer. For convex distortion cost functions with convex constraints, the minimization is formulated as a convex optimization problem. In the limit of a continuum of infinite layers, the minimum expected distortion is given by the solution to a set of linear differential equations in terms of the density of the fading distribution. As the bandwidth ratio b (channel uses per source symbol) tends to zero, the power distribution that minimizes expected distortion converges to the one that maximizes expected capacity. While expected distortion can be improved by acquiring CSI at the transmitter (CSIT) or by increasing diversity from the realization of independent fading paths, at high SNR the performance benefit from diversity exceeds that from CSIT, especially when b is large.Comment: Accepted for publication in IEEE Transactions on Information Theor

Minimum Expected Distortion in Gaussian Layered Broadcast Coding with Successive Refinement

A transmitter without channel state information (CSI) wishes to send a delay-limited Gaussian source over a slowly fading channel. The source is coded in superimposed layers, with each layer successively refining the description in the previous one. The receiver decodes the layers that are supported by the channel realization and reconstructs the source up to a distortion. In the limit of a continuum of infinite layers, the optimal power distribution that minimizes the expected distortion is given by the solution to a set of linear differential equations in terms of the density of the fading distribution. In the optimal power distribution, as SNR increases, the allocation over the higher layers remains unchanged; rather the extra power is allocated towards the lower layers. On the other hand, as the bandwidth ratio b (channel uses per source symbol) tends to zero, the power distribution that minimizes expected distortion converges to the power distribution that maximizes expected capacity. While expected distortion can be improved by acquiring CSI at the transmitter (CSIT) or by increasing diversity from the realization of independent fading paths, at high SNR the performance benefit from diversity exceeds that from CSIT, especially when b is large.Comment: To appear in the proceedings of the 2007 IEEE International Symposium on Information Theory, Nice, France, June 24-29, 200

Joint Source-Channel Codes for MIMO Block Fading Channels

We consider transmission of a continuous amplitude source over an L-block Rayleigh fading $M_t \times M_r$ MIMO channel when the channel state information is only available at the receiver. Since the channel is not ergodic, Shannon's source-channel separation theorem becomes obsolete and the optimal performance requires a joint source -channel approach. Our goal is to minimize the expected end-to-end distortion, particularly in the high SNR regime. The figure of merit is the distortion exponent, defined as the exponential decay rate of the expected distortion with increasing SNR. We provide an upper bound and lower bounds for the distortion exponent with respect to the bandwidth ratio among the channel and source bandwidths. For the lower bounds, we analyze three different strategies based on layered source coding concatenated with progressive, superposition or hybrid digital/analog transmission. In each case, by adjusting the system parameters we optimize the distortion exponent as a function of the bandwidth ratio. We prove that the distortion exponent upper bound can be achieved when the channel has only one degree of freedom, that is L=1, and $\min\{M_t,M_r\}=1$. When we have more degrees of freedom, our achievable distortion exponents meet the upper bound for only certain ranges of the bandwidth ratio. We demonstrate that our results, which were derived for a complex Gaussian source, can be extended to more general source distributions as well.Comment: 36 pages, 11 figure

Progressive Linear Precoder Optimization for MIMO Packet Retransmissions

This paper investigates the optimal linear precoder design for packet retransmissions in multi-input-multi-output (MIMO) systems. To fully utilize the time diversity provided by automatic repeat request (ARQ), we derive a sequence of successive optimal linear ARQ precoders for flat fading MIMO channels, which minimize the mean-square error between the transmitted data and the joint receiver output. The optimization is subject to an overall transmit power constraint. This progressive linear ARQ precoder combines the appropriate power loading and the optimal pairing of channel matrix singular values in the current retransmission with previous transmissions. This optimal pairing is a special feature unique to our sequential ARQ precoding approach. Simulation results demonstrate the effectiveness of this optimized ARQ precoding in reducing symbol MSE and detection bit-error rate