Could you explain the concept of Byte Pair Encoding (BPE) in natural language processing? Describe how BPE works as a subword tokenization technique, including the process of merging byte pairs, handling out-of-vocabulary words, and its application in text compression and language modeling. Additionally, discuss the trade-offs associated with using BPE compared to other tokenization methods and its effectiveness in capturing morphological variations and handling rare words in different languages.