Nature Is Analog
The information that is missing in the quantized signal is lost and cannot be restored.
The Saturation Effect of Digital Transmission Systems
Digital transmission systems have many well-known advantages, one of which is lossless transmission. However, this only holds for signals that are discrete in the first place (e.g., text) or have already been quantized by a source encoder. For analog input signals, the quantization error induced by the source encoder remains even if all bits are transmitted correctly. This results in a saturation effect for good channel conditions: Unless additional transmissions occur (whose request might require a feedback channel) the decoder is limited to the quality of the source encoder, regardless of the possibly great channel quality.
Hybrid Digital-Analog (HDA) Transmission
Even if a digital channel use is replaced by the transmission of the quantization error, the transmission quality of the resulting system is improved. More ...
Analog Modulo Block Codes
Another method is to avoid quantization at all by applying an analog channel coding technique. Inspired by digital block codes, analog modulo block codes use a generator matrix A to add redundancy to the information symbols. In order to limit the transmission power (and thus obtain a coding gain), a modulo function is applied after the multiplication with the matrix.
The generator matrix consists of a systematic part (unity matrix) and a parity part. The entries in the parity part are designed to amplify the input signal. When this amplification is reversed in the decoder, this is also applied to the channel noise, which is thus attenuated. However, the amplification would imply an increased transmission energy, which is circumvented by applying a (symmetric) modulo operation that limits the amplified value to a certain range.
The valid code words of analog modulo block codes are located on lines or (hyper-)planes that are parallel to each other (“branches”). This property can be exploited for decoding the received symbols. First, the closest branch to the received point is determined. With the knowledge of the branch, the effect of the modulo-function can be undone. Consecutively, the decoding is completed with a multiplication with the pseudo-inverse of the generator matrix.
More details can be found in [Schmitz15] and the other publications.
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