Rate-Energy Optimal Probabilistic Shaping Using Linear Codes.

Probabilistic shaping methods induce a desired nonuniform distribution on the transmitted symbols in order to realize a favorable trade-off between the communication rate and average transmission energy. In this work, we study a probabilistic shaping architecture wherein the central component is a binary linear code, employed as a lossy source code. The rate-distortion performance of the linear code directly determines the realized shaping rate-energy performance. We use this connection to establish the rate-energy optimality of the investigated shaping architecture. Although the primary focus of this paper is on shaping for two-symbol alphabets, extensions to non-binary alphabets will be briefly discussed.