Summary:

 - BIP 158  false positive rate is low, we can achieve lower bandwidth with higher false positive rate filter while sync blockchain

 - BIP 158 not do not support filter batching by design of used parameters for siphash and Golomb coding optimal parameters

 - Alternative compression with delta coding and splitting data to 2 bit string  sequences. First for data without prefixes, second one for information about  bit length written to first sequence.

   Second sequence have a lot of duplicates,  compressed with 2 round of Huffman algorithm. (Effectivity about 98% vs Golomb with optimal parameters)

 - Block filters batching reduce filter size significantly

- Separation of filters by address type allows lite client not to download redundant information without compromising privacy.

- Lite client filters download strategy: get biggest filter (smallest blocks/size rate) for blocks range, in case positive test  -> get medium filters to reduce blocks range ->  get block filters for affected range -> download affected blocks over TOR 

Implementation (python): https://github.com/bitaps-com/pybtc/blob/bugfix/pybtc/functions/filters.py#L172

Exactly information from mainnet  about size for separated filters by address types and batch size will be added within few days.

Thanks for any feedback.

      Aleksey Karpov