Moment Balancing Templates: Constructions to Add Insertion/Deletion Correction Capability to Error Correcting or Constrained Codes

Moment Balancing Templates for $(d,k)$-Constrained Codes and Run-Length Limited Sequences

“…Based on the Varshamov-Tenengolts construction in (3), we propose a moment balancing template to encode a binary code C of length K into a single insertion or deletion error correcting code. As shown in [2], [3] and [4], the binary code C can be any one of: an arbitrary random sequence, or an error correcting code, or a DC-free code, or a spectral null code, or a (d, k) constrained sequence with…”

“…Here n r is the number of codewords v in C that have σ(v) ≡ r (mod m). A universal moment balancing template is defined in [2] for the code C with an arbitrary moment distribution, in which the number of moment balancing bits n − K is bounded from below by log 2 m . For a code having a certain narrower range of moment values, such as one in which for some r's we have n r = 0, we can implement an optimized moment balancing template, which may introduce less redundancy than that of the universal template.…”

“…From (2) it follows that the first-order moment of a (d, k) sequence is completely determined by the indices of the 1's.…”

“…However, as shown in [1], insertion or deletion errors cause catastrophic problems for these systems. To protect a transmission system from a single insertion/deletion error, Ferreira et al [2] presented a moment balancing scheme, in which a linear error correcting codeword is further encoded in order to obtain a single insertion/deletion error correcting capability. However, preserving the constraint properties and keeping the redundancies within a practical-interest range make moment balancing templates of constrained codes more complicated.…”

“…Ferreira et al [2] also presented the moment balancing template for DC-free sequences and the template for (d, k) sequences with d = 1 and d = 2. Cheng, Ferreira and Ouahada [3], [4] presented the moment balancing template for further spectral null codes as introduced in [5].…”