On Compress-Forward without Wyner-Ziv Binning for Relay Networks

Noisy network coding is recently proposed for the general multi-source network by Lim, Kim, El Gamal and Chung. This scheme builds on compress-forward (CF) relaying but involves three new ideas, namely no Wyner-Ziv binning, relaxed simultaneous decoding and message repetition. In this paper, using the two-way relay channel as the underlining example, we analyze the impact of each of these ideas on the achievable rate region of relay networks. First, CF without binning but with joint decoding of both the message and compression index can achieve a larger rate region than the original CF scheme for multi-destination relay networks. With binning and successive decoding, the compression rate at each relay is constrained by the weakest link from the relay to a destination; but without binning, this constraint is relaxed. Second, simultaneous decoding of all messages over all blocks without uniquely decoding the compression indices can remove the constraints on compression rate completely, but is still subject to the message block boundary effect. This boundary effect is caused by the decoding of signal received in the last block, in which not all inputs and outputs may be regularly involved. Third, message repetition is necessary to overcome this boundary effect and achieve the noisy network coding region for multi-source networks. The rate region is enlarged with increasing repetition times. We also apply CF without binning specifically to the one-way and two-way relay channels and analyze the rate regions in detail. For the one-way relay channel, it achieves the same rate as the original CF and noisy network coding but has only 1 block decoding delay. For the two-way relay channel, we derive the explicit channel conditions in the Gaussian and fading cases for CF without binning to achieve the same rate region or sum rate as noisy network coding. These analyses may be appealing to practical implementation because of the shorter encoding and decoding delay in CF without binning.