# Correspondences Between Variable Length Parsing and Coding Problems

## Abstract

Stubley and Blake’s minimum discrimination parse tree problem is seen to correspond to Karp’s variable length unequal costs coding problem for arbitrary source distributions in the sense that, where Stubley and Blake minimize the discrimination *D*(*P ∥ Q*),Karp minimizes *D*(*Q ∥ P*)*.* In the special case that *Q* is uniform, Stubley and Blake’s problem is Tunstall parsing and Karp’s problem is Varn coding. In the special case that *P* is dyadic, Stubley and Blake’s problem is of interest because Karp’s problem is Huffman coding.

Similarly, Lempel, Even, and Cohn’s parse tree problem can be interpreted as minimizing *G*(*P* ∥ *Q*) for a particular functional *G* in the special case that *P* is dyadic. The problem of minimizing *G*(*P ∥ Q*) for arbitrary *P* is seen to correspond to Karp’s problem in the sense that Karp also minimizes *G*(*Q ∥ P*)*.* In the special case that *Q* is uniform, Tunstall parsing and Varn coding correspond to each other, and in the special case that *P* is dyadic, Lempel, Even, Cohn parsing and Huffman coding correspond to each other.

## Key words

Variable-length-to-block source coding block-to-variable-length source coding unequal costs coding parse tree Stubley and Blake algorithm Lempel Even and Cohn algorithm Karp algorithm Tunstall algorithm Varn algorithm Huffman algorithm## Preview

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