Coding Schemes for Multiple-Relay Channels

In network information theory, the relay channel models a communication scenario where there is one or more relay nodes that can help the information transmission between the source and the destination. Although the capacity of the relay channel is still unknown even in the single-relay case, two fundamentally different relay schemes have been developed by (Cover and El Gamal, 1979) for such channels, which, depending on whether the relay decodes the information or not, are generally known as Decode-and-Forward (D-F) and Compress-and-Forward (C-F). In the D-F relay scheme, the relay first decodes the message sent by the source and then forwards it to the destination, and the destination decodes the message taking into account the inputs of both the source and the relay. In contrast, the C-F relay scheme is used when the relay cannot decode the message sent by the source, but still can help by compressing its observation into some compressed version, and forwarding this compression into the destination; the destination then either successively or jointly decodes the compression of the relay’s observation and the original message of the source. For the single-relay case, it is known that joint compression-message decoding, although providing more freedom in choosing the compression at the relay, cannot achieve higher rates for the original message than successive decoding. This thesis addresses some fundamental issues in generalizing and unifying the above D-F and C-F relay schemes to the multiple-relay case. We first generalize the C-F scheme to multiple-relay channels, and investigate the question of whether compression-message joint decoding can improve the achievable rate compared to successive decoding in the multiple-relay case. It is demonstrated that in the case of multiple relays, there is no improvement on the achievable rate by joint decoding either. More interestingly, it is discovered that any compressions not supporting successive decoding will actually lead to strictly lower achievable rates for the original message. Therefore, to maximize the achievable rate for the original message, the compressions should always be chosen to support successive decoding. Further-