Optimal Encoding Schemes for Several Classes of Discrete Degraded Broadcast Channels
Consider a memoryless Degraded Broadcast Channel (DBC) in which the channel output is a single-letter function of the channel input and the channel noise. As examples, for the Gaussian Broadcast Channel (BC) this single-letter function is regular Euclidian addition and for the binary-symmetric BC this single-letter function is Galois-Field-two addition. This paper identifies several classes of discrete memoryless DBCs for which a relatively simple encoding scheme, which the authors call natural encoding, achieves capacity. Natural Encoding (NE) combines symbols from independent codebooks (one for each receiver) using the same single-letter function that adds distortion to the channel. The alphabet size of each NE codebook is bounded by that of the channel input.