Optimal nonuniform signaling for Gaussian channels

• Published in: IEEE transactions on information theory Vol. 39; no. 3; pp. 913 - 929
• Main Authors: Kschischang, F.R., Pasupathy, S.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.05.1993; Institute of Electrical and Electronics Engineers
• Subjects: Amplitude modulation; Applied sciences; Bit rate; Coding, codes; Constellation diagram; Data communication; Entropy; Exact sciences and technology; Gaussian channels; Information, signal and communications theory; Modulation coding; Probability distribution; Signal and communications theory; Signal design; Telecommunications and information theory; Transmitters; Probability law; Variable; Coding; Gaussian channel; Huffman code; Data transmission; Method of maximum entropy; Transmission rate; Variable length code
• ISSN: 0018-9448; 1557-9654
• DOI: 10.1109/18.256499

Variable-rate data transmission schemes in which constellation points are selected according to a nonuniform probability distribution are studied. When the criterion is one of minimizing the average transmitted energy for a given average bit rate, the best possible distribution with which to select constellations points is a Maxwell-Boltzmann distribution. In principle, when constellation points are selected according to a Maxwell-Boltzmann distribution, the ultimate shaping gain ( pi e/6 or 1.53 dB) can be achieved in any dimension. Nonuniform signaling schemes can be designed by mapping simple variable-length prefix codes onto the constellation. Using the Huffman procedure, prefix codes can be designed that approach the optimal performance. These schemes provide a fixed-rate primary channel and a variable-rate secondary channel, and are easily incorporated into standard lattice-type coded modulation schemes.< >