Low-complexity maximum-likelihood decoding of shortened enumerativepermutation codes for holographic storage

摘要

Volume holographic memories (VHM) are page-oriented opticalnstorage systems whose pages commonly contain on the order of one millionnpixels. Typically, each stored data page is composed of an equal numbernof binary pixels in either a low-contrast (“off”) state or anhigh-contrast (“on”) state. By increasing the number ofn“off” pixels and decreasing the number of “on”npixels per page, there is an associated gain in VHM system storagencapacity. When grayscale pixels are used, a further gain is possible bynsimilarly controlling the fraction of pixels at each gray level. Thisnpaper introduces a constant-weight, nonbinary, shortened enumerativenpermutation modulation block code to produce pages that exploit thenproposed capacity advantage. In addition to the code description, wenpresent an encoder and a low-complexity maximum-likelihood (ML) decodernfor the shortened permutation code. A proof verifies our claim of MLndecoding. Applying this class of code to VHMs predicts a 49% increase innstorage capacity when recording modulation coded 3-bit (eight graynlevel) pixels compared with a VHM using a binary signaling alphabet andnequal-probable (unbiased) data