Predict the complete cost

Counts 8,4,2,2; prefix lengths 1,2,3,3.

Compute payload before adding a one-byte header.

Resolve the prediction

Payload = 8+8+6+6 = 28 bits, padded to 4 bytes.

Fixed two-bit symbols also occupy 4 bytes. With a one-byte header, the modeled representation occupies 5.

Expected length and complete file length answer different questions.

Spend the prefix budget

Lengths [1,2,3,3]: 1/2+1/4+1/8+1/8 = 1.

Try adding another length-three symbol: the sum exceeds one.

An unused branch is allowed; an overlapping prefix is not.

Same counts, different order

Compare AAAABBBB with ABABABAB.

A byte histogram cannot distinguish their structure. A context or dictionary model can.

A zero-probability prediction for a possible byte leaves no representation unless an escape rule exists.

Transfer task

A 40-bit model header saves two payload bits per symbol.

Twenty symbols tie before padding; twenty-one first improve bit cost. Then round each total to bytes.

For [6,3,3] at lengths [1,2,2], verify 18 payload bits and 1.5 bits/symbol.