Quantifying the Loss of Compress–Forward Relaying Without Wyner–Ziv Coding

Abstract

The compress-and-forward (CF) strategy achieves the optimal diversity-multiplexing tradeoff (DMT) of a three-node half-duplex relay network in slow fading, under the assumption that the relay has perfect knowledge of all three channel coefficients and that the relay makes use of Wyner-Ziv (WZ) source coding with side information. This paper studies the achievable DMT of the same network when the relay is constrained to make use of standard (non-WZ) source coding. Under a short-term power constraint at the relay, using source coding without side information results in a significant loss in terms of the DMT. For multiplexing gains <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</i> les <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> / <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> , this loss can be fully compensated for by using power control at the relay. On the contrary, for <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</i> isin ( <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> / <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> ,1), the loss with respect to WZ coding remains significant.