Approximate lattice decoding offers an excellent tradeoff between error performance and computational complexity for multi-input multi-output (MIMO) communication. However, its remarkable performance largely remains a mystery to date. This paper takes a step towards analytically characterizing its performance. To this aim, we define the proximity factors of approximate lattice decoding, which measure the gap to maximum-likelihood (ML) decoding in signal-to-noise ratio (SNR) for given error rate. The proximity factors are derived and found to be bounded above by a function of the dimension of the lattice alone. As a direct consequence, it follows that lattice decoding can always achieve full diversity of MIMO fading channels.
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