Optimal Rate-Constrained Transcoding for a 2:1 Bandwidth Reducing Shannon Mapping

For a wireless system we assume that we are free to design the transmitter and receiver from the ground up, enabling the use of continuous-amplitude systems like Shannon mappings. Transport networks on the other hand are standardised and packet based, requiring a digital representation. In this paper a simple and effective scheme for transcoding, or digitising, the 2:1 bandwidth reducing Shannon mapping is proposed. This enables communication over heterogeneous networks without having to decode the Shannon mapping and re-encode with a digital source coder. It is shown that a simple uniform scalar quantizer operating on the one-dimensional channel symbols can outperform a 2-D entropy-constrained vector quantizer operating on the decoded signals from the Shannon mapping. The quantization can be performed either at the transmitter side, or at the receiver side. Both approaches are only 2.8 dB away from the theoretical optimum when operating at the channel capacity