Abstract
In this work, we consider the zero-delay transmission of bivariate Gaussian sources over a Gaussian broadcast channel with one-bit analog-to-digital converter (ADC) front ends. An outer bound on the conditional distortion region is derived. Focusing on the minimization of the average distortion, two types of methods are proposed to design nonparametric mappings. The first one is based on the joint optimization between the encoder and decoder with the use of an iterative algorithm. In the second method, we derive the necessary conditions to develop the optimal encoder numerically. Using these necessary conditions, an algorithm based on gradient descent search is designed. Subsequently, the characteristics of the optimized encoding mapping structure are discussed, and inspired by which, several parametric mappings are proposed. Numerical results show that the proposed parametric mappings outperform the uncoded scheme and previous parametric mappings for broadcast channels with infinite resolution ADC front ends. The nonparametric mappings succeed in outperforming the parametric mappings. The causes for the differences between the performances of two nonparametric mappings are analyzed. The average distortions of the parametric and nonparametric mappings proposed here are close to the bound for the cases with one-bit ADC front ends in low channel signal-to-noise ratio regions.
Highlights
Accepted: 8 December 2021Traditional digital communication systems, based on Shannon’s separation principle between source and channel coding [1], concentrate on mappings with long block lengths. these separated systems are not very robust to the channel variation, optimality can be achieved given that no constraints are considered in terms of complexity and delay.these systems have become unsuitable for certain emerging applications that require transmission in extreme latency constraints, such as those involving the internet of things (IoT) technologies [2] or wireless sensor networks (WSNs) [3]
In this work, considering extremely low delay and low energy consumption requirements, we focus on the zero-delay JSCC communications system for a bivariate Gaussian source over a bandwidth-matched Gaussian broadcast channel with two receivers
The overall mean squared error (MSE) is still defined as D = 21 ( D1 + D2 ), and signal-todistortion rate (SDR) is defined as 10 log10
Summary
Traditional digital communication systems, based on Shannon’s separation principle between source and channel coding [1], concentrate on mappings with long block lengths. In [24], Morteza et al considered the zero-delay transmission of a Gaussian source over an AWGN channel with one-bit ADC front end and correlated side information at the receiver. In this work, considering extremely low delay and low energy consumption requirements, we focus on the zero-delay JSCC communications system for a bivariate Gaussian source over a bandwidth-matched Gaussian broadcast channel with two receivers. Both of the receivers are equipped with a one-bit ADC front end. To the best of our knowledge, there is no previous work that derives the necessary condition of the optimal encoder for the transmission of correlated Gaussian sources over the broadcast channel with onebit ADC front ends. Q(·) denotes the complementary cumulative distribution function of the standard normal distribution
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