res more computation labor. Although the LLL LR algorithm has known average complexity for some cases [@Daude1994; @Ling2007], its average complexity for our case is unknown, and the worst-case complexity could be unbounded [@Jalden2008].

-   The quantized search (QS) method developed by Sakzad [*et al.*]{} in [@Sakzad2012]. The search consists of two phases: 1) an integer $\alpha_0$ between 1 and $\floor{P^{1/2}}$ that provides the maximum rate is selected as the initial value of the amplifying factor $\alpha$; 2) the amplifying factor is then refined by searching in $[\alpha_0-1,\alpha_0+1]$ with a step size 0.1. After the amplifying factor $\alpha$ is determined, the coefficient vector $\a$ is set as $\round{\alpha\h}$. An improved version of the QS method is the quantized exhaustive search (QES) method proposed in [@Sakzad2014], which was developed for complex-valued channels.

-   The rounding method that simply sets the coefficient vector by rounding the channel vector to an integer-valued vector.

As shown in Figure \[figure:Rate\], the optimal methods, i.e., the BnB method and the SG method, always provide the highest average computation rates for all dimensions and over the whole SNR regime, as expected. The LLL method provides close-to-optimal average computation rates. Our proposed QPR method also offers close-to-optimal average computation rates for almost all the dimensions and SNR values considered, except that its performance degrades a little bit for high dimensions at high SNR as shown in Figure \[figure:Rate\_L16\]. The performance of our QPR method improves slightly compared with the version we presented in [@Zhou2014; @Wen2015]. The reason is that here we initialize the output coefficient vector as $[0,\cdots,0,1]^T$, which definitely results non-zero computation rate, while in the previous version the output coefficient vector could result zero computation rate.

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Finally, we demonstrate the efficiency of the proposed QPR method by comparing the running time of finding the coefficien