Channel Coding and Source Coding With Increased Partial Side Information

Abstract

Let ( S 1 , i , S 2 , i ) ∼ i . i . d p ( s 1 , s 2 ) , i = 1 , 2 , ⋯ be a memoryless, correlated partial side information sequence. In this work, we study channel coding and source coding problems where the partial side information ( S 1 , S 2 ) is available at the encoder and the decoder, respectively, and, additionally, either the encoder’s or the decoder’s side information is increased by a limited-rate description of the other’s partial side information. We derive six special cases of channel coding and source coding problems and we characterize the capacity and the rate-distortion functions for the different cases. We present a duality between the channel capacity and the rate-distortion cases we study. In order to find numerical solutions for our channel capacity and rate-distortion problems, we use the Blahut-Arimoto algorithm and convex optimization tools. Finally, we provide several examples corresponding to the channel capacity and the rate-distortion cases we presented.

Keywords

• Blahut–Arimoto algorithm
• channel capacity
• channel coding
• duality
• Gelfand–Pinsker channel coding
• partial side information
• rate-distortion
• source coding
• Wyner-Ziv source coding