Hybrid digital-analog coding with bandwidth expansion for correlated Gaussian sources under Rayleigh fading

EURASIP Journal on Advances in Signal Processing, May 2017

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.

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Hybrid digital-analog coding with bandwidth expansion for correlated Gaussian sources under Rayleigh fading

Yahampath EURASIP Journal on Advances in Signal Processing Hybrid digital-analog coding with bandwidth expansion for correlated Gaussian sources under Rayleigh fading Pradeepa Yahampath 0 0 Department of Electrical and Computer Engineering, University of Manitoba , Winnipeg, MB R3T 5V6 , Canada 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. Hybrid digital-analog coding; Predictive quantization; Transform coding; Fading channels; Speech coding 1 Introduction 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. If the channel-state information (CSI) is available, the transmitter can adapt coding and modulation to maintain the optimal performance at all times. However, there are common situations in which the transmitter adaptation is not an option. One obvious example is broadcasting where a single transmitter sends information to multiple receivers. Since the channels to different receivers may not be the same, it is not possible to adapt the transmitter to a specific channel state. Another example is when there is no possibility of CSI feedback from a mobile receiver to the transmitter. In either case, the receiver suffers from the “cliff effect” [1]—when channel signal-to-noise ratio (CSNR) decreases, at some point, a less than 1 dB drop in CSNR can take the decoder from perfect operation to complete failure (threshold effect), and when the CSNR increases from this point, the decoder output quality remains fixed regardless of the CSNR (see for example [2] (Fig. 5)). One solution to this problem is multi-resolution coding and modulation [1, 3, 4]. This scheme does not entirely eliminate the cliff effect but improves it to a stair-case effect. For analog sources, a better alternative is hybrid digital-analog (HDA) coding [1, 5, 6] which is the focus of this paper. It is known that uncoded or analog transmission achieves the optimal performance theoretically attainable (OPTA) in MMSE sense when both the source and the channel are Gaussian and memoryless and have the same bandwidths [7]. Clearly, uncoded transmission cannot be optimal for sources with memory and when the source and channel bandwidths are not matched. For sources with memory, widely used digital source-coding techniques such as predictive quantization (PQ) transform coding (TC) [8] exploit source memory to achieve a coding gain and will outperform uncoded transmission © The Author(s). 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. if both the transmitter and the receiver have CSI. However, systems based on these techniques still suffer from the aforementioned cliff effect when the transmitter has no CSI. On the other hand, implementing good analog codes for sources with memory is difficult. A promising approach to benefit from both the robustness of analog transmission against CSNR variations and the sourcecoding gain due to source correlation is HDA coding. Fundamentally, HDA transmission involves the simultaneous transmission of a source in both digital and analog forms. Most previous work on HDA coding have used a form of layered transmission in which the base layer is digitally coded, and the quantization error of the base layer is transmitted as a refinement layer, using analog pulse amplit (...truncated)


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Pradeepa Yahampath. Hybrid digital-analog coding with bandwidth expansion for correlated Gaussian sources under Rayleigh fading, EURASIP Journal on Advances in Signal Processing, 2017, pp. 37, Volume 2017, Issue 1, DOI: 10.1186/s13634-017-0474-z