Design and performance of BICM-ID systems with hypercube constellations

Abstract

This paper introduces new mappings of QPSK symbols, viewed as a multi-dimensional hypercube, to improve the performance of bit-interleaved coded modulation with iterative decoding (BICM-ID). By evaluating the upper bound of the bit error rate performance of BICM-ID, a condition to find the best mapping of a hypercube constellation in terms of the asymptotic performance under different channel models is established. A general and simple algorithm to construct the best mapping of a hypercube is then proposed. Analytical and simulation results show that the use of the proposed mappings together with very simple convolutional codes can offer significant coding gains over the conventional BICM-ID systems for all the channel models considered. Such coding gains are achieved without any bandwidth nor power expansion and with a very small increase in the system complexity.

EXIT Charts for System Design and Analysis

“…13, Gray Mapping (GM) does not provide any iteration gain upon increasing the MI at the input of the demapper. However, using the multi-dimensional hupercube labelling defined for QPSK in [75,76], which we refer to as Anti-Gray Mapping (AGM) 2 , results in different EXIT characteristics, as illustrated by the continuous line seen in Fig. 13.…”

“…Several papers studied the multi-dimensional constellation labelling demonstrating that it was beneficial to invoke multidimensional modulation in the context of both TCM and BICM [76,[86][87][88]. However, these papers did not quantify the achievable improvement, neither did they detail whether the improvement was merely due to the increased number of bits used by the combined symbols allowing for more flexibility in the design of the constellation , or due to the beneficial multi-dimensional labelling.…”

Tight error bound for coded unitary space-time modulation

“…Furthermore, it is easy to verify that this optimal mapping is any mapping that satisfies the following condition: As mentioned before, there is a strong similarity between the unitary constellation Ψ and the hypercube constellation considered in [16], [20]. In fact, the mapping that satisfies Condition 1 can easily be obtained by modifying the best mapping for the 4-dimensional hypercube constellation in [16], [20]. The procedure to obtain the best mapping is stated as follows (the proof is omitted): …”

“…Owning to the success of decoding step as normally seen in the analysis of BICM-ID systems [15], [16], it can be assumed that the labels of two unitary signal points Ψ e andΨ e differ in only 1 bit. Furthermore, observe that ∆ e are i.i.d.…”

“…By studying the distance profile between the signal points in Ψ, it is not hard to recognize that the structure of Ψ is very similar to the structure of a 4-dimensional hypercube [16], [20], although the distances considered for the 4-dimensional hypercube in [16], [20] are the Euclidean distances. More specifically, the following facts about chordal distance can be established for any signal point Ψ l ∈ Ψ.…”