On Multidimensional BICM-ID Constellation Labelling

Abstract

-It is widely recognised that the choice of a specific bit-to-symbol mapping scheme or a beneficial constellation labelling is an influential factor, when designing bit-interleaved coded modulation using iterative decoding (BICM-ID) for the sake of achieving a high iteration gain. Generally, a larger constellation size of a higher-dimensional space renders the bit-to-symbol mapping design more flexible. In this paper, we first define a flexibility measure based on the extrinsic information transfer (EXIT) characteristics of bit-to-symbol mapping schemes. Secondly, we investigate the effect of expanding the constellation to a higher-dimensional space on our proposed EXIT characteristic flexibility index, when transmitting diverse numbers of bits per joint symbol.

EXIT Charts for System Design and Analysis

“…It was shown in [84] that the flexibility improvement of the bit-to-symbol mapping offered by expanding the modulation constellation to a higherdimensional space, when communicating over a Rayleigh channel was mainly due to the increased number of bits-perjoint-symbol. Nonetheless, useful EXIT flexibility improvements may also be obtained by expanding the modulation constellation to a higher-dimensional space, especially when communicating over an independent fading based Rayleigh channel [84].…”

“…Hence, in [84] an EXIT chart based flexibility measure was introduced for analysing the effect of expanding the constellation to a higherdimensional space by jointly transmitting a pair of symbols of a classic two-dimensional constellation.…”

“…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. In [84], a flexibility measure was proposed based on EXIT charts, where investigations were carried out into the effect of expanding the constellation to more dimensions as well as to quantify the benefits of increasing the classic constellation order. It was shown in [84] that the flexibility improvement of the bit-to-symbol mapping offered by expanding the modulation constellation to a higherdimensional space, when communicating over a Rayleigh channel was mainly due to the increased number of bits-perjoint-symbol.…”

“…In [84], a flexibility measure was proposed based on EXIT charts, where investigations were carried out into the effect of expanding the constellation to more dimensions as well as to quantify the benefits of increasing the classic constellation order. It was shown in [84] that the flexibility improvement of the bit-to-symbol mapping offered by expanding the modulation constellation to a higherdimensional space, when communicating over a Rayleigh channel was mainly due to the increased number of bits-perjoint-symbol. Nonetheless, useful EXIT flexibility improvements may also be obtained by expanding the modulation constellation to a higher-dimensional space, especially when communicating over an independent fading based Rayleigh channel [84].…”

“…It is widely recognised that the choice of a specific bit-tosymbol mapping scheme or a beneficial constellation labelling is an influential factor, when designing Bit-Interleaved Coded Modulation using Iterative Decoding (BICM-ID) for the sake of achieving a high iteration gain [24,84,85]. Hence, in [84] an EXIT chart based flexibility measure was introduced for analysing the effect of expanding the constellation to a higherdimensional space by jointly transmitting a pair of symbols of a classic two-dimensional constellation.…”