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Many binary code embedding techniques have been proposed for large-scale approximate nearest neighbor search in computer vision. Recently, product quantization that encodes the cluster index in each subspace has been shown to provide impressive accuracy for nearest neighbor search. In this paper, we explore a simple question: is it best to use all the bit budget for encoding a cluster index in each subspace? We have found that as data points are located farther away from the centers of their clusters, the error of estimated distances among those points becomes larger. To address this issue, we propose a novel encoding scheme that distributes the available bit budget to encoding both the cluster index and the quantized distance between a point and its cluster center. We also propose two different distance metrics tailored to our encoding scheme. We have tested our method against the-state-of-the-art techniques on several well-known benchmarks, and found that our method consistently improves the accuracy over other tested methods. This result is achieved mainly because our method accurately estimates distances between two data points with the new binary codes and distance metric.

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