  In this thesis, the infrared structure of squared matrix elements in quantum
chromodynamics (QCD) is scrutinised. Specifically, the triple-collinear
splitting functions are decomposed and improvements to antenna subtraction are
sought through the construction of idealised antenna functions. The
antenna-subtraction technique has demonstrated remarkable effectiveness in
handling next-to-next-to-leading order (NNLO) infrared divergences for a wide
range of QCD processes relevant for colliders. However, since antenna functions
were historically extracted from matrix elements, they did not have uniform
properties, which made the generation of subtraction terms complex. Antenna
subtraction up to NNLO is reviewed, including the role of antenna functions. A
general algorithm is detailed in order to re-build antenna functions, with
idealised features, directly from a specified list of unresolved limits, for
any number of real and virtual emissions. Using this general algorithm,
together with the decomposition of the triple-collinear splitting functions,
all the antenna functions required for NNLO QCD calculations in the final-final
configuration are constructed and it is demonstrated that they form a
consistent NNLO subtraction scheme. The idealised antenna functions should
simplify the generation of subtraction terms and minimise the introduction of
spurious limits. Additionally, the general algorithm sets out an initial
blueprint for next-to-NNLO (N$^3$LO) idealised antennae for use in N$^3$LO QCD
calculations.
