A new high performance turbo encoder scheme for bandwidth efficient modulation

Constellation shaping can provide an energy saving called shaping gain. The idea behind constellation shaping is that signals with large norm are used less frequently than signals with small norm, thus improving the overall gain by adding shaping gain to the original coding gain [1]. Theoretically, when constellation points are selected according to a continuous Gaussian distribution at every dimension, the maximum shaping gain of πe 6 = 1.53 dB can be achieved in the limit for infinite transmission rates. Practically, a smaller gain can be achieved in finite constellations. Many shaping techniques for the Gaussian channel are known in the literature. It was first shown by Gallager [2] that binary codes can be used for mappings of nonequiprobable letters that achieve capacity on an arbitrary discrete memoryless channel. Calderbank and Ozarow [3] introduced subconstellation partitioning. In this approach a signal constellation is partitioned into several subconstellations, points in the same subconstellation are used equiprobably, and a shaping code selects the subconstellations with various frequencies. Forney [4] introduced trellis shaping. This method uses a search through the trellis diagram of a shaping convolutional code for selecting the constellation points. Kschischang and Pasupathy [5] took a different approach by mapping simple variable-length prefix codes onto the constellation. A similar method that uses subdivision of the signal constellation into variable-size regions was proposed by Livingston [6]. For Gaussian channels, turbo coded modulation techniques can be broadly classified into binary schemes and Turbo Trellis Coded Modulation (TTCM) [7]. The first group can be further divided into “pragmatic” schemes with a single component binary turbo code, and multilevel binary turbo codes [8]. The pragmatic approach [9] is simple and versatile and is much less complex to design and to implement than TTCM. In this paper we combine nonuniform signaling with the pragmatic binary turbo coded modulation environment. Our shaping method follows the technique proposed by Gallager in his 1968 book on information theory [2]. This technique can be easily applied to any binary turbo or turbo-like code, including parallel, serial and Low Density Parity Check (LDPC) codes. The nonequiprobable letters are obtained by using a table that maps b–bits equiprobable input words onto nonequiprobable m–bits M–ary PAM (or equivalently M QAM) symbols, at rates 2 and 3 bits/dim.