CM and BICM limits for rectangular constellations
The classical Shannon capacity limit is well-known to communications engineers. It is useful in setting an absolute limit to what can be achieved in conveying information through a channel affected by additive white Gaussian noise, the concept of channel capacity. However, certain practical choices made in designing systems for communication and broadcasting implicitly set intrinsic tighter limits, which makes it more difficult to assess how well a practically implemented system is performing unless these tighter limits are known and understood. The concepts of Coded Modulation (CM) and Bit-Interleaved Coded Modulation (BICM) capacity limits have been presented by other workers. This paper first explores their implications on systems using uniform QAM (quadrature amplitude modulation) of various orders. The way that these CM and BICM limits for uniform QAM systematically fall short of the classical Shannon limit leads to the idea that non-uniform QAM could offer better capacity. This idea is pursued, with results that show a significant increase in BICM capacity, reducing the shortfall from the classical Shannon limit, for carefully optimised non-uniform constellations having sizes up to 4096-QAM.
The observation that some points in these optimised non-uniform QAM constellations tend to merge leads to a new concept, Condensed QAM, having fewer states than the ‘parent’ non-uniform QAM yet suffering negligible drop in capacity. This makes it feasible to optimise condensed versions of larger constellations still, where direct optimisation of the full non-uniform constellations would not be tractable. Results are thereby obtained for the optimisation of various condensations of 16384-QAM. The shortfall in BICM capacity from unconstrained Shannon capacity is then a mere 0.071 bit/symbol, at a design SNR of 22 dB (alternatively expressible as being 0.214 dB from the limit).
These results and their implications are then placed in context with a brief discussion of some other results from the literature.
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