In upstream vectored DSL systems using zero-forcing generalized decision feedback equalizers (ZF-GDFE), different decoding orders cause performance tradeoffs among the users. In this paper, these tradeoffs are characterized by formulating optimization problems with practical constraints. Lagrange dual decomposition and a two-step algorithm are used to solve the dual problems optimally with the computational complexity linear in the number of DMT tones. However, solving the tonal subproblem, which is shared by all the proposed optimization problems, associates with a high-complexity exhaustive search of K\ orderings, where K is the number of users. Thus, this paper proposes two low-complexity algorithms in order to find suboptimal orderings: successive ordering search (SOS) with complexity O(K <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> ) and modified greedy search (MGA) with complexity O(K <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> ). Numerical results show that MGA performs well enough in finding the achievable rate region. For problems related to feasibility check, SOS is suitable for closely approximating the optimal solution.
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