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In the setting of quasi-static Multiple-Input Multiple-Output (MIMO) channels, the authors consider the high Signal-to-Noise Ratio (SNR) asymptotic complexity required by the Sphere Decoding (SD) algorithm for decoding a large class of full rate linear space-time codes. With SD complexity being a function of the code and having random fluctuations with varying channel, noise and code-words, the introduced SD complexity exponent manages to concisely describe the computational reserves required by the SD algorithm to achieve arbitrarily close to optimal performance in decoding the codes. It is worth noting that, to date, this asymptotically describes the minimum known complexity required for a decoder and time-out policy to provably allow a gap to maximum likelihood performance that vanishes for increasing SNR.
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