Polar Code Design for Noisy Blackwell Channels

In this letter, we introduce a class of discrete memoryless broadcast channels, called noisy Blackwell channels, which generalize the Blackwell channel to include noise and to more than two users. We design the polar code for the noisy Blackwell channel based on Marton's coding scheme. We choose auxiliary random variables and the mapping from auxiliary random variables to the channel input, such that the sum-rate capacity can be achieved very closely. Furthermore, we show that the designed polar code can be applied to multi-level cell flash memories for improving random I/O performance. The simulation results demonstrate that our designed polar codes achieve good performance even for a large number of users.