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)