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

• Published in: IEEE journal on selected areas in communications Vol. 19; no. 4; pp. 783 - 790
• Main Authors: King, B.M., Neifeld, M.A.
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.04.2001; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Block codes; Decoding; Encoders; Gain; Gray-scale; Holographic optical components; Holography; Information retrieval; Information storage; Maximum likelihood decoding; Memory; Modulation; Modulation coding; Optical modulation; Optical recording; Permutations; Pixels; Storage capacity
• ISSN: 0733-8716; 1558-0008
• DOI: 10.1109/49.920186

Volume holographic memories (VHM) are page-oriented optical storage systems whose pages commonly contain on the order of one million pixels. Typically, each stored data page is composed of an equal number of binary pixels in either a low-contrast ("off") state or a high-contrast ("on") state. By increasing the number of "off" pixels and decreasing the number of "on" pixels per page, there is an associated gain in VHM system storage capacity. When grayscale pixels are used, a further gain is possible by similarly controlling the fraction of pixels at each gray level. This paper introduces a constant-weight, nonbinary, shortened enumerative permutation modulation block code to produce pages that exploit the proposed capacity advantage. In addition to the code description, we present an encoder and a low-complexity maximum-likelihood (ML) decoder for the shortened permutation code. A proof verifies our claim of ML decoding. Applying this class of code to VHMs predicts a 49% increase in storage capacity when recording modulation coded 3-bit (eight gray level) pixels compared with a VHM using a binary signaling alphabet and equal-probable (unbiased) data.