Optimal zero-delay coding (quantization) of R-d-valued linearly generated Markov sources is studied under quadratic distortion. The structure and existence of deterministic and stationary coding policies that are opti...
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Optimal zero-delay coding (quantization) of R-d-valued linearly generated Markov sources is studied under quadratic distortion. The structure and existence of deterministic and stationary coding policies that are optimal for the infinite horizon average cost (distortion) problem are established. Prior results studying the optimality of zero-delay codes for Markov sources for infinite horizons either considered finite alphabet sources or, for the Rd-valued case, only showed the existence of deterministic and non-stationary Markov coding policies or those which are randomized. In addition to existence results, for finite blocklength (horizon) T the performance of an optimal coding policy is shown to approach the infinite time horizon optimum at a rate O(1/T). This gives an explicit rate of convergence that quantifies the near-optimality of finite window (finite-memory) codes among all optimal zero-delay codes.
In this paper, we consider the problem of zero-delay (encoding a single-source sample) robust joint source-channel coding over an additive white Gaussian noise channel. We propose a new scheme that, unlike previously ...
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In this paper, we consider the problem of zero-delay (encoding a single-source sample) robust joint source-channel coding over an additive white Gaussian noise channel. We propose a new scheme that, unlike previously known coding schemes, achieves the optimal scaling of the source signal-to-distortion ratio (SDR) versus channel signal-to-noise ratio (SNR). Also, we propose a family of robust codes, which together maintain a bounded gap with the optimum SDR curve (in terms of decibel). To show the importance of this result, we derive some theoretical bounds on the asymptotic performance of a widely used class of delay-limited hybrid digital-analog (HDA) coding schemes based on superposition of analog and digital components. We show that, unlike the delay-unlimited case, for this class of delay-limited HDA codes, the asymptotic performance loss is unbounded (in terms of decibels). Although the main focus of this paper is on uniform sources, it is also shown that the results are also valid for a more general class of well-behaved distributions.
Consider the following communication scenario. An encoder observes a stochastic process and causally decides when and what to transmit about it, under a constraint on the expected number of bits transmitted per second...
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Consider the following communication scenario. An encoder observes a stochastic process and causally decides when and what to transmit about it, under a constraint on the expected number of bits transmitted per second. A decoder uses the received codewords to causally estimate the process in real time. The encoder and the decoder are synchronized in time. For a class of continuous Markov processes satisfying regularity conditions, we find the optimal encoding and decoding policies that minimize the end-to-end estimation mean-square error under the rate constraint. We show that the optimal encoding policy transmits a 1-bit codeword once the process innovation passes one of two thresholds. The optimal decoder noiselessly recovers the last sample from the 1-bit codewords and codeword-generating time stamps, and uses it to decide the running estimate of the current process, until the next codeword arrives. In particular, we show the optimal causal code for the Ornstein-Uhlenbeck process and calculate its distortion-rate function. Furthermore, we show that the optimal causal code also minimizes the mean-square cost of a continuous-time control system driven by a continuous Markov process and controlled by an additive control signal.
Consider the following communication scenario. An encoder observes a stochastic process and causally decides when and what to transmit about it, under a constraint on bits transmitted per second. A decoder uses the re...
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ISBN:
(纸本)9781728164328
Consider the following communication scenario. An encoder observes a stochastic process and causally decides when and what to transmit about it, under a constraint on bits transmitted per second. A decoder uses the received codewords to causally estimate the process in real time. The encoder and the decoder are synchronized in time. We aim to find the optimal encoding and decoding policies that minimize the end-to-end estimation mean-square error under the rate constraint. For a class of continuous Markov processes satisfying regularity conditions, we show that the optimal encoding policy transmits a 1-bit codeword once the process innovation passes one of two thresholds. The optimal decoder noiselessly recovers the last sample from the 1-bit codewords and codeword-generating time stamps, and uses it as the running estimate of the current process, until the next codeword arrives. In particular, we show the optimal causal code for the Ornstein-Uhlenbeck process and calculate its distortion-rate function.
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