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Previous work by the authors on parity-preserving fixed-length constrainedencoders is extended to the variable-length case. Parity-preservingvariable-length encoders are formally defined, and, to this end, Kraftconditions are developed for the parity-preserving variable-length setting.Then, a necessary and sufficient condition is presented for the existence ofdeterministic parity-preserving variable-length encoders for a givenconstraint. Examples are provided that show that there are coding ratios whereparity-preserving variable-length encoders exist, while fixed-length encodersdo not.

Variable-Length Constrained Coding and Kraft Conditions: The Parity-Preserving Case