  Consider a general quantum source that emits at discrete time steps quantum
pure states which are chosen from a finite alphabet according to some
probability distribution which may depend on the whole history. Also, fix two
positive integers $m$ and $l$. We encode any tensor product of $ml$ many states
emitted by the quantum source by breaking it into $m$ many blocks where each
block has length $l$, and considering sequences of $m$ many isometries so that
each isometry encodes one of these blocks into the Fock space, followed by the
concatenation of their images. We only consider certain sequences of such
isometries that we call "special block codes" in order to ensure that the the
string of encoded states is uniquely decodable. We compute the minimum average
codeword length of these encodings which depends on the quantum source and the
integers $m$, $l$, among all possible special block codes. Our result extends
the result of [Bellomo, Bosyk, Holik and Zozor, Scientific Reports 7.1 (2017):
14765] where the minimum was computed for one block, i.e. for $m=1$.
