Trellis Shaping
摘要
As the last chapter directly linked to the trellis of convolutional codes, Trellis Shaping is introduced, which makes it possible to achieve the ultimate shaping gain by reducing the average power with a Viterbi algorithm at the transmitter and the energy of symbols as the required positive additive metric. Trellis shaping reduces the average power by restricting high (infinitely)-dimensional signals by a sphere, which means a Gaussian distribution in one or two dimensions. At the same time, the Gaussian distribution optimizes the Mutual Information for the AWGN channel. The chapter contains one- and multi-dimensional Trellis-Shaping designs, where the latter is a must for one-dimensional signal sets, and also shows that Trellis Shaping can be applied for more general optimization tasks, as long as a positive and additive metric can be formulated. Line-coding is presented as an application example.