Joint Source-Channel Coding with Time-Varying Channel and Side-Information

Transmission of a Gaussian source over a time-varying Gaussian channel is studied in the presence of time-varying correlated side information at the receiver. A block fading model is considered for both the channel and the side information, whose states are assumed to be known only at the receiver. The optimality of separate source and channel coding in terms of average end-to-end distortion is shown when the channel is static while the side information state follows a discrete or a continuous and quasiconcave distribution. When both the channel and side information states are time-varying, separate source and channel coding is suboptimal in general. A partially informed encoder lower bound is studied by providing the channel state information to the encoder. Several achievable transmission schemes are proposed based on uncoded transmission, separate source and channel coding, joint decoding as well as hybrid digital-analog transmission. Uncoded transmission is shown to be optimal for a class of continuous and quasiconcave side information state distributions, while the channel gain may have an arbitrary distribution. To the best of our knowledge, this is the first example in which the uncoded transmission achieves the optimal performance thanks to the time-varying nature of the states, while it is suboptimal in the static version of the same problem. Then, the optimal \emph{distortion exponent}, that quantifies the exponential decay rate of the expected distortion in the high SNR regime, is characterized for Nakagami distributed channel and side information states, and it is shown to be achieved by hybrid digital-analog and joint decoding schemes in certain cases, illustrating the suboptimality of pure digital or analog transmission in general.Comment: Submitted to IEEE Transactions on Information Theor

On optimum parameter modulation-estimation from a large deviations perspective

We consider the problem of jointly optimum modulation and estimation of a real-valued random parameter, conveyed over an additive white Gaussian noise (AWGN) channel, where the performance metric is the large deviations behavior of the estimator, namely, the exponential decay rate (as a function of the observation time) of the probability that the estimation error would exceed a certain threshold. Our basic result is in providing an exact characterization of the fastest achievable exponential decay rate, among all possible modulator-estimator (transmitter-receiver) pairs, where the modulator is limited only in the signal power, but not in bandwidth. This exponential rate turns out to be given by the reliability function of the AWGN channel. We also discuss several ways to achieve this optimum performance, and one of them is based on quantization of the parameter, followed by optimum channel coding and modulation, which gives rise to a separation-based transmitter, if one views this setting from the perspective of joint source-channel coding. This is in spite of the fact that, in general, when error exponents are considered, the source-channel separation theorem does not hold true. We also discuss several observations, modifications and extensions of this result in several directions, including other channels, and the case of multidimensional parameter vectors. One of our findings concerning the latter, is that there is an abrupt threshold effect in the dimensionality of the parameter vector: below a certain critical dimension, the probability of excess estimation error may still decay exponentially, but beyond this value, it must converge to unity.Comment: 26 pages; Submitted to the IEEE Transactions on Information Theor

Source-Channel Diversity for Parallel Channels

We consider transmitting a source across a pair of independent, non-ergodic channels with random states (e.g., slow fading channels) so as to minimize the average distortion. The general problem is unsolved. Hence, we focus on comparing two commonly used source and channel encoding systems which correspond to exploiting diversity either at the physical layer through parallel channel coding or at the application layer through multiple description source coding. For on-off channel models, source coding diversity offers better performance. For channels with a continuous range of reception quality, we show the reverse is true. Specifically, we introduce a new figure of merit called the distortion exponent which measures how fast the average distortion decays with SNR. For continuous-state models such as additive white Gaussian noise channels with multiplicative Rayleigh fading, optimal channel coding diversity at the physical layer is more efficient than source coding diversity at the application layer in that the former achieves a better distortion exponent. Finally, we consider a third decoding architecture: multiple description encoding with a joint source-channel decoding. We show that this architecture achieves the same distortion exponent as systems with optimal channel coding diversity for continuous-state channels, and maintains the the advantages of multiple description systems for on-off channels. Thus, the multiple description system with joint decoding achieves the best performance, from among the three architectures considered, on both continuous-state and on-off channels.Comment: 48 pages, 14 figure

Lossy joint source-channel coding in the finite blocklength regime

This paper finds new tight finite-blocklength bounds for the best achievable lossy joint source-channel code rate, and demonstrates that joint source-channel code design brings considerable performance advantage over a separate one in the non-asymptotic regime. A joint source-channel code maps a block of $k$ source symbols onto a length$-n$ channel codeword, and the fidelity of reproduction at the receiver end is measured by the probability $\epsilon$ that the distortion exceeds a given threshold $d$. For memoryless sources and channels, it is demonstrated that the parameters of the best joint source-channel code must satisfy $nC - kR(d) \approx \sqrt{nV + k \mathcal V(d)} Q(\epsilon)$, where $C$ and $V$ are the channel capacity and channel dispersion, respectively; $R(d)$ and $\mathcal V(d)$ are the source rate-distortion and rate-dispersion functions; and $Q$ is the standard Gaussian complementary cdf. Symbol-by-symbol (uncoded) transmission is known to achieve the Shannon limit when the source and channel satisfy a certain probabilistic matching condition. In this paper we show that even when this condition is not satisfied, symbol-by-symbol transmission is, in some cases, the best known strategy in the non-asymptotic regime