Abstract
Consider communicating a correlated Gaussian source over a Rayleigh fading channel with no knowledge of the channel signal-to-noise ratio (CSNR) at the transmitter. In this case, a digital system cannot be optimal for a range of CSNRs. Analog transmission however is optimal at all CSNRs, if the source and channel are memoryless and bandwidth matched. This paper presents new hybrid digital-analog (HDA) systems for sources with memory and channels with bandwidth expansion, which outperform both digital-only and analog-only systems over a wide range of CSNRs. The digital part is either a predictive quantizer or a transform code, used to achieve a coding gain. Analog part uses linear encoding to transmit the quantization error which improves the performance under CSNR variations. The hybrid encoder is optimized to achieve the minimum AMMSE (average minimum mean square error) over the CSNR distribution. To this end, analytical expressions are derived for the AMMSE of asymptotically optimal systems. It is shown that the outage CSNR of the channel code and the analog-digital power allocation must be jointly optimized to achieve the minimum AMMSE. In the case of HDA predictive quantization, a simple algorithm is presented to solve the optimization problem. Experimental results are presented for both Gauss-Markov sources and speech signals.
Highlights
In digital communication over a fading channel, the best performance is achieved when both the transmitter and the receiver are adapted to the channel state
7 Conclusions This paper presented an approach to designing hybrid digital-analog (HDA)-predictive quantization (PQ) and HDA-transform coding (TC) systems for transmitting correlated Gaussian sources over frequency-flat, block Rayleigh fading channels, when channel-state information (CSI) is not available to the transmitter
The main issue addressed in this paper is the joint optimization of the analog-digital power allocation and the outage channel signal-to-noise ratio (CSNR) to minimize the average MMSE (AMMSE) of HDA-PQ and HDA-TC systems
Summary
In digital communication over a fading channel, the best performance is achieved when both the transmitter and the receiver are adapted to the channel state. For highly correlated sources, the HDA systems can substantially outperform both purely digital and purely analog transmission over a wide range of receiver CSNRs. 1.1 Main contribution and related previous work Compared to previous work on HDA coding of Gaussian sources with memory, the main contribution of this paper is the joint optimization of power allocation and quantization rate of HDA systems based on PQ or TC, with respect to the AMMSE criterion. Yu et al [9] present similar HDA scheme for video transmission based on H.264/AVC codec but use channel superposition of analog and digital components the power allocation between which is determined by assuming a worst-case CSNR.
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