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Capacity of a Class of Diamond Channels



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Capacity of a Class of Diamond Channels Wei Kang Sennur Ulukus Department of Electrical and Computer Engineering University of Maryland College Park MD 20742 wkang eng umd edu ulukus umd edu Abstract We study a special class of diamond channels which was introduced by Schein in 2001 In this special class each diamond channel consists of a transmitter a noisy relay a noiseless relay and a receiver We prove the capacity of this class of diamond channels by providing an achievable scheme and a converse The capacity we show is strictly smaller than the cut set bound Our result also shows the optimality of a combination of decode and forward DAF and compress andforward CAF at the noisy relay node This is the first example where a combination of DAF and CAF is shown to be capacity achieving Finally we note that there exists a duality between this diamond channel coding problem and the Kaspi Berger source coding problem I P ROBLEM S TATEMENT AND THE R ESULT The diamond channel was first introduced by Schein in 2001 1 The diamond channel consists of one transmitter two relays and a receiver where the transmitter and the two relays form a broadcast channel as the first stage and the two relays and the receiver form a multiple access channel as the second stage The capacity of the diamond channel in its most general form is open Schein explored several special cases of the diamond channel one of which 1 Section 3 5 is specified as follows see Figure 1 The multiple access channel consists of two orthogonal links with rate constraints R1 and R2 respectively The broadcast channel contains a noisy branch and a noiseless branch i e with input X and two outputs X and Y We refer to the relay node receiving Y as the noisy relay and the relay node receiving X as the noiseless relay Schein provided two achievable schemes for this class of diamond channels In this paper we will prove the capacity of this special class of diamond channels The formal definition of the problem is as



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