Bounds on The Capacity of The Bit-Shift Magnetic Recording Channel

Shlomo Shamai (Shitz), Ephraim Zehavi

Research output: Contribution to journalArticlepeer-review

29 Scopus citations


A simple statistical channel model is suggested to account for single position bit shifts that have been identified to be one of the major impairments in magnetic recording. We investigate bounds on the capacity of this channel where the channel inputs are the (d, k) codes, commonly used in magnetic recordings. for d ≥ 2, this channel is conveniently described in terms of phrase lengths where a bit shift causes a phrase either to shrink or to expand. The inherent correlation present in consecutive shift-affected phrases introduces memory into the channel model. Sequences of nondecreasing lower bounds and nonincreasing upper bounds on the capacity are evaluated and investigated for a variety of parameters. Lower bounds on the zero-error capacity are also studied. The channel model is extended to a concatenated scheme of a bit shift channel connected in tandem with the binary symmetric channel, thus capturing both major error generating mechanisms—the bit shifts as well as randomly generated errors. Lower and upper bounds on the capacity of this concatenated channel model with (d,k) input sequences are derived and discussed.

Original languageEnglish
Pages (from-to)863-872
Number of pages10
JournalIEEE Transactions on Information Theory
Issue number3
StatePublished - May 1991
Externally publishedYes

Bibliographical note

Funding Information:
Manuscript received March 7, 1990, revised November 18, 1990. This work was supported by the Fund for the Promotion of Research at the Technion. This work was presented in part at the IEEE International Symposium on Information Theory, San Diego, CA, January 14-19, 1990; and in part at GLOBECOMPO, San Diego, CA, December 2-5, 1990. The authors are with the Department of Electrical Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel. IEEE Log Number 9143364.


  • Bit-shift channel
  • capacity
  • error capacity
  • magnetic recording
  • zero


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