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.
Highlights
In this paper, we investigate point-to-point channel models and rate-distortion problem models where both users have different and correlated partial side information and where, in addition, a rate-limited description of one of the user’s side information is delivered to the other user.We show the duality between the channel models and the rate-distortion models we investigate.For the convenience of the reader, we refer to the state information as the side information, to the partial side information that is available to the encoder as the encoder’s side information (ESI) and to the partial side information that is available to the decoder as the decoder’s side information (DSI).We refer ro the rate-limited description of the other user’s side information as the increase in the side information
Case 1: The encoder is informed with ESI and the decoder is informed with increased DSI
Case 2: The encoder is informed with increased ESI and the decoder is informed with DSI
Summary
We investigate point-to-point channel models and rate-distortion problem models where both users have different and correlated partial side information and where, in addition, a rate-limited description of one of the user’s side information is delivered to the other user. The encoder and the decoder do not know S perfectly, but they each possess a version of S; the encoder knows S1 (the ESI) and the decoder knows S2 (the DSI) For this example, let us assume that the source of the interruption is physically located in close proximity to the encoder (potentially, both signal sources are co-located). We assume that the transmitter can provide a rate-limited description of the ESI, S1 , to the decoder, increasing his DSI. In these circumstances, we pose the question; what is the capacity of the channel between the encoder and the decoder?. It allows one to design better practical codes, like polar codes and LDPC codes
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