Hybrid Digital-Analog Coding

The transmission of continuous-amplitude (analog) and discrete-time source samples is considered. “Analog” signifies continuous-amplitude, while, of course, all signal processing is done digitally with precision depending on the corresponding architecture. These source samples could e.g. be a sensor signal such as a microphone signal, a temperature or could also be a continuous-amplitude parameter which is the result of a parametric coder.

Usually, these continuous-amplitude samples (u) are quantized in a source encoder. Then the bits are channel encoded, modulated and then transmitted (y) over a channel and disturbed by channel noise (n). Please note that this channel is discrete time, but it is again analog!

The performance of such a system can be measured in pSNR which is the end to end signal to noise ratio. The channel quality is denoted in cSNR.

At a certain channel quality, all bits are transmitted correctly and the source samples are reconstructed with the fidelity which is given by the quantizer in the source encoder. Further improvements in channel quality cannot improve the pSNR anymore, and hence a saturation effect can be noted:

The design of purely digital systems is dictated by the worst case channel condition for which the system still should work. Most of the time, the system experiences a better channel quality, but it cannot exploit it.

The aim of Hybrid Digital Analog (HDA) transmission systems is to eliminate this saturation. The key is to additionally transmit the quantization error using analog methods.

The source symbols are transmitted in the same way as in the purely digital system, but the quantization error (u^a) is also obtained at the transmitter. An analog mapper employs an energy normalization using e.g. a linear mapping (A=M) leading to analog channel symbols. The digital modulation symbols and the analog channel symbols are multiplexed and transmitted over the analog channel. At the receiver, the digital part is decoded as usual and the Analog Demapper estimates the quantization error using e.g. a Linear Minimum Mean Square Error (LMMSE) estimator.

Please note that the overall number of channel uses (N) is kept constant for a comparison to a purely digital system. Also the transmission energy and the number of source symbols (M) is the same. The key to design a competitive HDA system is to employ a quantizer with a lower fidelity than in the purely digital system. This allows using the same channel encoder and modulator to still transmit with the same number of channel uses (N) while additionally transmitting the quantization error.

Since the analog quantization error is directly transmitted over an analog channel, the transmission fidelity of the HDA system improves with increasing channel quality and thus, the saturation effect is eliminated: