Confidence Intervals of the Simulations

The codebook ${\rm W}_{\Lambda _{24}}$ was optimized according to Table III-A and its performance was evaluated with 500,000 i.i.d. Gaussian random samples blocked into 20,000 25-dimensional vectors and encoded as in Table III. The lattice encoding used the Leech lattice nearest neighbor algorithm in [41]. The quality of the simulation results is expressed in terms of a 95% confidence interval. The simulation run of 20,000 vectors was broken down into 20 blocks of 1,000 vectors. For each block, the average distortion was determined. Applying the central limit theorem to each block distortion and using the students $t$-distribution, we calculated the 95% confidence interval. For each simulation, these intervals were found to be less than 0.03 dB.