Designing Nonlinear Turbo Codes with a Target Ones Density

Certain binary asymmetric channels, such as Z-channels in which one of the two crossover probabilities is zero, demand optimal ones densities different from 50%. Some broadcast channels, such as broadcast binary symmetric channels (BBSC) where each component channel is a binary symmetric channel, also require a non-uniform input distribution due to the superposition coding scheme, which is known to achieve the boundary of capacity region. This paper presents a systematic technique for designing nonlinear turbo codes that are able to support ones densities different from 50%. To demonstrate the effectiveness of our design technique, we design and simulate nonlinear turbo codes for the Z-channel and the BBSC. The best nonlinear turbo code is less than 0.02 bits from capacity

Optimal Natural Encoding Scheme for Discrete Multiplicative Degraded Broadcast Channels

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 broadcas