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Lee Metric Codes for Detecting and Correcting Errors due to Insertion and/or Deletion of 0's in Runlength Constrained Sequences

IP.com Disclosure Number: IPCOM000115774D
Original Publication Date: 1995-Jun-01
Included in the Prior Art Database: 2005-Mar-30
Document File: 2 page(s) / 60K

Publishing Venue

IBM

Related People

Roth, RM: AUTHOR [+2]

Abstract

Disclosed is a new application of p-ary codes for the Lee metric. The application is directed to the detection and correction of bitshift and synchronization errors induced by the insertion and/or the deletion of 0's in binary, runlength constrained sequences. These sequences are commonly used in digital data recording.

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Lee Metric Codes for Detecting and Correcting Errors due to Insertion
and/or Deletion of 0's in Runlength Constrained Sequences

      Disclosed is a new application of p-ary codes for the Lee
metric.  The application is directed to the detection and correction
of bitshift and synchronization errors induced by the insertion
and/or
the deletion of 0's in binary, runlength constrained sequences.
These
sequences are commonly used in digital data recording.

      The coding method makes use of the sequence r of runlengths
associated to a constrained binary sequence.  These runlengths are
mapped in a specified manner to a sequence of p-ary symbols.  An
insertion or deletion of a symbol 0 into the binary sequence
translates into an increment or decrement by 1 in a corresponding
runlength in r.  This, in turn, generates an error of Lee weight 1 in
the associated p-ary sequence.  As part of this invention, the p-ary
sequence will be composed of codewords from an error-correcting code
for the Lee metric.  A p-ary code with minimum Lee distance d can
simultaneously correct b bitshift errors and s non-bitshift
synchronization errors whenever 2b + s is less than or equal to
(d-1)/2.

      The advantage of the Lee metric codes over the more traditional
Hamming weight codes proposed in the prior art [*]  is that,
typically, codes for the Hamming metric require two check symbols per
(Hamming) error corrected, while Lee metric codes require only one
check symbol per (Le...