Power Preserving 2:1 Bandwidth Reduction Mappings

In this work we consider dimension reducing mappings that can be used for joint source-channel coding (JSCC) systems. In such systems, the source coding and the channel coding is performed as a single operation. Although it is known by Shannon´s separation theorem that asymptotically JSCC is not required for attaining the optimal performance, utilizing such schemes is beneficial for practical reasons such as delay and implementation simplicity. We specifically focus on the bandwidth reduction case, where the bandwidth of the data is greater than the bandwidth of the channel. More specifically, we focus on bandwidth reduction mappings, where the JSCC operation is performed using a single nonlinear operation. A modification of the spiral mapping is presented, so the power at the output is proportional to that of the input