Optimal natural encoding scheme for discrete multiplicative degraded broadcast channels

Abstract

Abstract-Certain degraded broadcast channels (DBCs) have the property that the boundary of the capacity region can be achieved by an encoder that combines independent codebooks (one for each receiver) using the same singleletter function that adds distortion to the channel. We call this the natural encoder for the DBC. Natural encoders are known to achieve the capacity region boundary of the broadcast Gaussian channel, and the broadcast binary-symmetric channel. Recently, they have also been shown to achieve the capacity region of the broadcast Z channel. This paper shows that natural encoding achieves the capacity region boundary for discrete multiplicative DBCs. The optimality of the natural encoder also leads to a relatively simple expression for the capacity region for discrete multiplicative DBCs.Index Terms-Conditional entropy bound, degraded broadcast channel, discrete multiplicative degraded broadcast channel, natural encoding

Designing Nonlinear Turbo Codes with a Target Ones Density

“…These codes were designed using the traditional Hamming distance metric and also performed near capacity. The presented design techniques for nonlinear turbo codes could also be extended to general group-addition degraded broadcast channels [19] as future work.…”