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

Joint source channel coding for non-ergodic channels: the distortion signal-to-noise ratio (SNR) exponent perspective

We study the problem of communicating a discrete time analog source over a channel such that the resulting distortion is minimized. For ergodic channels, Shannon showed that separate source and channel coding is optimal. In this work we study this problem for non-ergodic channels. Although not much can be said about the general problem of transmitting any analog sources over any non-ergodic channels with any distortion metric, for many practical problems like video broadcast and voice transmission, we can gain insights by studying the transmission of a Gaussian source over a wireless channel with mean square error as the distortion measure. Motivated by different applications, we consider three different non-ergodic channel models - (1) Additive white Gaussian noise (AWGN) channel whose signal-to-noise ratio (SNR) is unknown at the transmitter; (2) Rayleigh fading multiple-input multiple-output MIMO channel whose SNR is known at the transmitter; and (3) Rayleigh fading MIMO channel whose SNR is unknown at the transmitter. The traditional approach to study these problems has been to fix certain SNRs of interest and study the corresponding achievable distortion regions. However, the problems formulated this way have not been solved even for simple setups like 2 SNRs for the AWGN channel. We are interested in performance over a wide range of SNR and hence we use the distortion SNR exponent metric to study this problem. Distortion SNR exponent is defined as the rate of decay of distortion with SNR in the high SNR limit. We study several layered transmissions schemes where the source is first compressed in layers and then the layers are transmitted using channel codes that provide variable error protection. Results show that in several cases such layered transmission schemes are optimal in terms of the distortion SNR exponent. Specifically, if the band- width expansion (number of channel uses per source sample) is b, we show that the optimal distortion SNR exponent for the AWGN channel is b and it is achievable using a superposition based layered scheme. For the L-block Rayleigh fading M x N MIMO channel the optimal exponent is characterized for b < (|N - M|+1)= min(M;N) and b > MNL2. This corresponds to the entire range of b when min(M;N) = 1 and L = 1. The results also show that the exponents obtained using layered schemes which are a small subclass of joint source channel coding (JSCC) schemes are, surprisingly, as good as and better in some cases than achievable exponent of all other JSCC schemes reported so far

Side information aware source and channel coding in wireless networks

Signals in communication networks exhibit significant correlation, which can stem from the physical nature of the underlying sources, or can be created within the system. Current layered network architectures, in which, based on Shannon’s separation theorem, data is compressed and transmitted over independent bit-pipes, are in general not able to exploit such correlation efficiently. Moreover, this strictly layered architecture was developed for wired networks and ignore the broadcast and highly dynamic nature of the wireless medium, creating a bottleneck in the wireless network design. Technologies that exploit correlated information and go beyond the layered network architecture can become a key feature of future wireless networks, as information theory promises significant gains. In this thesis, we study from an information theoretic perspective, three distinct, yet fundamental, problems involving the availability of correlated information in wireless networks and develop novel communication techniques to exploit it efficiently. We first look at two joint source-channel coding problems involving the lossy transmission of Gaussian sources in a multi-terminal and a time-varying setting in which correlated side information is present in the network. In these two problems, the optimality of Shannon’s separation breaks down and separate source and channel coding is shown to perform poorly compared to the proposed joint source-channel coding designs, which are shown to achieve the optimal performance in some setups. Then, we characterize the capacity of a class of orthogonal relay channels in the presence of channel side information at the destination, and show that joint decoding and compression of the received signal at the relay is required to optimally exploit the available side information. Our results in these three different scenarios emphasize the benefits of exploiting correlated side information at the destination when designing a communication system, even though the nature of the side information and the performance measure in the three scenarios are quite different.Open Acces

Distortion exponent of parallel fading channels

We consider the end-to-end distortion achieved by transmitting a continuous amplitude source over M parallel, independent quasi-static fading channels. We analyze the high SNR expected distortion behavior characterized by the distortion exponent. We first give an upper bound for the distortion exponent in terms of the bandwidth ratio between the channel and the source assuming the availability of the channel state information at the transmitter. Then we propose joint source-channel coding schemes based on layered source coding and multiple rate channel coding. We show that the upper bound is tight for large and small bandwidth ratios. For the rest, we provide the best known distortion exponents in the literature. By suitably scaling the bandwidth ratio, our results would also apply to block fading channels. \ua9 2006 IEEE

Distortion Exponent of Parallel Fading Channels

Abstract — We consider the end-to-end distortion achieved by transmitting a continuous amplitude source over M parallel, independent quasi-static fading channels. We analyze the high SNR expected distortion behavior characterized by the distortion exponent. We first give an upper bound for the distortion exponent in terms of the bandwidth ratio between the channel and the source assuming the availability of the channel state information at the transmitter. Then we propose joint sourcechannel coding schemes based on layered source coding and multiple rate channel coding. We show that the upper bound is tight for large and small bandwidth ratios. For the rest, we provide the best known distortion exponents in the literature. By suitably scaling the bandwidth ratio, our results would also apply to block fading channels. I