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

Brian M. King, Mark A. Neifeld

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)783-790
Number of pages8
JournalIEEE Journal on Selected Areas in Communications
Issue number4
StatePublished - Apr 2001


  • DC codes
  • Enumeration code
  • Holographic data storage
  • Low weight codes
  • Modulation coding
  • Optical data storage
  • Page-oriented memories
  • Permutation code
  • Sparse codes

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Electrical and Electronic Engineering


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