2biBitCount

2biBitCount is a term used in some discussions of data encoding to describe the average number of bits required to represent two-bit blocks after applying a coding scheme. It is not a standard metric with broad consensus, and its exact interpretation can vary between texts. In general, it is described as the expected code length per two-bit block and is used to compare the efficiency of different block-encoding strategies for data that naturally arrives as two-bit symbols.

Definition and calculation: Let blocks B take values among {00, 01, 10, 11} with probabilities p00, p01, p10, p11. If each block is encoded into a binary codeword of length L(b) bits, the 2biBitCount is the average code length per block: H2 = sum over b of p_b times L(b). The units are bits per two-bit block. In a fixed-length encoding, H2 equals 2. With variable-length codes tailored to block probabilities, H2 can be less than 2, limited by the source entropy of two-bit blocks. It is distinct from the overall bit rate of a binary stream, which is computed per bit or per source symbol.

Relation and usage: 2biBitCount is used mainly in theoretical analyses of block coding and two-bit alphabets, where researchers compare how efficiently different encodings compress two-bit blocks. It should not be confused with the bit-count parameters used in image file formats or in other contexts, such as headers that refer to biBitCount. The term is informal and not widely standardized.

Example: Suppose a source emits 00 with probability 0.5, and 01, 10, 11 with probabilities 0.1667 each. If we assign code lengths L(00)=1, L(01)=2, L(10)=2, L(11)=2, then 2biBitCount ≈ 0.5×1 + 0.1667×2 + 0.1667×2 + 0.1667×2 ≈ 1.5 bits per two-bit block.