A setup involving zero-delay sequential transmission of a vector Markov source over a burst erasure channel is studied. A sequence of source vectors is compressed in a causal fashion at the encoder, and the resulting output is transmitted over a burst erasure channel. The destination is required to reconstruct each source vector with zero-delay, but those source sequences that are observed either during the burst erasure, or in the interval of length W following the burst erasure need not be reconstructed. The minimum achievable compression rate is called the rate-recovery function. We assume that each source vector is independent identically distributed (i.i.d.) across the spatial dimension and is sampled from a stationary, first-order Markov process across the temporal dimension. For discrete sources, the case of lossless recovery is considered, and upper and lower bounds on the rate-recovery function are established. Both these bounds can be expressed as the rate for predictive coding, plus a term that decreases at least inversely with the recovery window length W. For Gauss-Markov sources and a quadratic distortion measure, upper and lower bounds on the minimum rate are established when W = 0. These bounds are shown to coincide in the high resolution limit. Finally, another setup involving i.i.d. Gaussian sources is studied and the rate-recovery function is completely characterized in this case.

We introduce a framework to study fundamental limits of sequential coding of Markov sources under an error propagation constraint. An encoder sequentially compresses a sequence of vector-sources that are spatially i.i.d. but temporally correlated according to a Markov process. The channel erases up to B packets in a single burst, but reveals all other packets to the destination. The destination is required to reproduce all the source-vectors instantaneously and in a loss less manner, except those sequences that occur in a window of length B+W following the start of the erasure burst. We define a rate-recovery function R(B, W), the minimum compression rate that can be achieved in this framework, and develop upper and lower bounds for first-order Markov sources. For the special class of linear diagonally correlated deterministic sources, we propose a new coding technique--prospicient coding--that achieves the rate-recovery function. Finally, a lossy extension to the rate-recovery function is also studied for a class of Gaussian sources where the source is temporally and spatially i.i.d. and the decoder aims to recover a collection of past K sources with a quadratic distortion measure. The optimal rate-recovery function is compared with the sub-optimal techniques including forward error correction coding (FEC) and Wyner-Ziv coding, and performance gains are quantified.

A rateless code-i.e., a rate-compatible family of codes-has the property that codewords of the higher rate codes are prefixes of those of the lower rate ones. A perfect family of such codes is one in which each of the codes in the family is capacity-achieving. We show by construction that perfect rateless codes with low-complexity decoding algorithms exist for additive white Gaussian noise channels. Our construction involves the use of layered encoding and successive decoding, together with repetition using time-varying layer weights. As an illustration of our framework, we design a practical three-rate code family. We further construct rich sets of near-perfect rateless codes within our architecture that require either significantly fewer layers or lower complexity than their perfect counterparts. Variations of the basic construction are also developed, including one for time-varying channels in which there is no a priori stochastic model.

We consider the problem of transmission over an unknown time-varying Gaussian channel, whose signal-to-noise ratio (SNR) is constant within a block but varies arbitrarily between blocks. For this scenario, we develop efficient automatic repeat request (ARQ) protocols in the form of low-complexity rateless codes, which encode a message into a sequence of incremental redundancy blocks. Following the receipt of each redundancy block, the receiver feeds back to the transmitter the SNR experienced by that block, which the encoder makes use of in structuring subsequent blocks. The resulting architecture, which involves layered repetition encoding and successive cancellation decoding, is capacity-achieving, enabling the message to be recovered with the minimum possible number of blocks for the realized channel.

In this tutorial article we discuss some salient aspects of the wireless channel, and the challenges and opportunities they pose for streaming media. Streaming media has a number of fundamental characteristics that differentiate it from generic data for which most wireless data transport protocols are designed. This means that solutions designed for media distribution in wired contexts do not directly translate into appropriate wireless solutions: designers must jointly optimize for both media and wireless characteristics. Through a number of examples we discuss how channel, source, and application-dependent concepts such as multiuser diversity, opportunistic communications, loss tolerance, and differing application-dependent delay constraints can be exploited to pose new and useful constructs for streaming media over wireless