Unequal a-priori probabilities for holographic storage

Volume holographic memories (VHMs) can deliver high aggregate data rates at a slow page rate by placing on the order of one million pixels per holographic page. By reducing the number of `on' pixels per VHM data page we may increase the diffracted power into each pixel and therefore increase the number of pages we can store in our memory; although by doing so we have reduced the amount of user information per page. A detailed analysis shows that the information capacity can be increased by 15% with proper adjustment of the binary pixel priors such that a page contains about 25% `on' pixels. Enumeration block coding techniques allow us to adjust the data priors appropriately with a code rate near the entropy bound for long block lengths. The sparsity of `on' pixels also helps to reduce the effects of inter-pixel crosstalk by strongly reducing the probability that worst-case pixel patterns (e.g., blocks of `on' pixels with the center pixel `off') will occur in the data page. In addition, enumeration coding offers low encoding/decoding latency that scales linearly with the number of pixels per page. In this paper we discuss the theoretical advantage of optimum prior selection, as well as experimental results in achieving this capacity gain. The experiments verify that it is practical to adjust the priors and that an overall capacity gain of around 17% can be achieved for a realistic VHM system.