Abstract
In this paper, we introduce the zero-delay multiple-description problem, where an encoder constructs two descriptions and the decoders receive a subset of these descriptions. The encoder and decoders are causal and operate under the restriction of zero delay, which implies that at each time instance, the encoder must generate codewords that can be decoded by the decoders using only the current and past codewords. For the case of discrete-time stationary scalar Gauss—Markov sources and quadratic distortion constraints, we present information-theoretic lower bounds on the average sum-rate in terms of the directed and mutual information rate between the source and the decoder reproductions. Furthermore, we show that the optimum test channel is in this case Gaussian, and it can be realized by a feedback coding scheme that utilizes prediction and correlated Gaussian noises. Operational achievable results are considered in the high-rate scenario using a simple differential pulse code modulation scheme with staggered quantizers. Using this scheme, we achieve operational rates within // of the theoretical lower bounds for varying description rates.
Highlights
Real-time communication is desirable in many modern applications, e.g., Internet of Things [1], audio transmission for hearing aids [2], stereo audio signals [3], on-line video conferencing [4], or systems involving feedback, such as networked control systems [5,6,7]
We study a lower bound on the sum-rate of the ZDMD coding problem with feedback, which only depends on the joint statistics of the source encoder input, X, and the decoder outputs, Y (i) i = 0, 1, 2
We studied the ZDMD source coding problem where the multiple descriptions (MDs) encoder and decoders are required to be causal and of zero delay
Summary
Real-time communication is desirable in many modern applications, e.g., Internet of Things [1], audio transmission for hearing aids [2], stereo audio signals [3], on-line video conferencing [4], or systems involving feedback, such as networked control systems [5,6,7] All these scenarios may operate under strict requirements on latency and reliability. Some compression (reproduction quality) is sacrificed for an overall lower latency [9] Despite their potential advantages over channel codes for certain applications, MD codes are rarely used in practical communication systems with feedback. The reasons are that from a practical point of view, good MD
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