On Achievable Rates for User Cooperation and Relay Channels

In this paper, we derive a new achievable rate region for the user cooperation channel, which exceeds the best known result for this channel [Wil83]. Since the user cooperation channel includes many other known channels as a special case, the new rate region provides an improved achievable rates for many of the special cases (discussed later). The most notable example is that of the Gaussian relay channel [CG79], for which we present a new closed form inner bound higher than the only known result (Theorem 5 in [CG79]). The basic idea of the proposed encoding and decoding scheme is easier to grasp for a simpler case, the relay channel, by keeping in mind the following Markovian scheme from [CG79]. In Markovian encoding, the relay decodes everything in the current block and uses it to establish a basis for common information sent from the transmitter and relay in the next block. The fact that Markovian coding does not achieve capacity depends on to two inter-related facts: (a) the relay decodes each codeword completely, and (b) discards the residual after decoding; this limits the relay channel capacity to the capacity between the source and the relay. Our proposed encoding does not require the relay to necessarily decode the whole codeword from the transmitter. In addition, the relay “source” encodes the whole received signal some implicit embedding of with the decoded information. Note that the signal transmitted by the relay is not separable into a source code and a channel code. For the user cooperation channel, the above operation is performed by both users for each others’ signal. Rest of the paper is organized as follows. We describe the user cooperation channel in Section 2. Then, we present the main result of the paper for discrete memoryless channels is presented in Section 3, including some special cases of the previously known sub-channels. Results on Gaussian user cooperation channel are presented in Section 4, which are used to improve the relay channel achievable rates in Section 5.