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Sphere Decoding Revisited
arXiv:2512.11195v1 Announce Type: new
Abstract: In this paper, the paradigm of sphere decoding (SD) for solving the integer least square problem (ILS) is revisited, where extra degrees of freedom are introduced to exploit the decoding potential. Firstly, the equivalent sphere decoding (ESD) is proposed, which is essentially the same with the classic Fincke-Pohst sphere decoding but characterizes the sphere radius $D>0$ with two new parameters named as initial searching size $K>1$ and deviation factor $\sigma>0$. By fixing $\sigma$ properly, we show that given the sphere radius $D\triangleq\sigma\sqrt{2\ln K}$, the complexity of ESD in terms of the number of visited nodes is upper bounded by $|S|
Abstract: In this paper, the paradigm of sphere decoding (SD) for solving the integer least square problem (ILS) is revisited, where extra degrees of freedom are introduced to exploit the decoding potential. Firstly, the equivalent sphere decoding (ESD) is proposed, which is essentially the same with the classic Fincke-Pohst sphere decoding but characterizes the sphere radius $D>0$ with two new parameters named as initial searching size $K>1$ and deviation factor $\sigma>0$. By fixing $\sigma$ properly, we show that given the sphere radius $D\triangleq\sigma\sqrt{2\ln K}$, the complexity of ESD in terms of the number of visited nodes is upper bounded by $|S|
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