  Block encoding is a data input model commonly used in a quantum computer. It
is an ingenious technique that embeds a matrix $A$ satisfying $\left\|A/ \alpha
\right\| \leq 1$ into a larger unitary matrix $U_{A}$. Its complexity can
affect the complexity of quantum algorithms in the framework of block encoding.
In this paper, a new base scheme of block encoding is given which generalizes
the one in \cite{camps2024explicit} by removing the constraint that every data
item should appear in all columns. And applying preamplification and state
preparation methods, the base scheme is further improved, which results in
lower \textit{figures of merit} than that in special case
\cite{sunderhauf2024block}. Then, the construction of oracles in block encoding
schemes are discussed in detail. Considering special sparse structured matrices
coming from ocean acoustics, two concrete examples are used to illustrate the
feasibility of the proposed base scheme of block encoding and their explicit
quantum circuits are implemented. Finally, the corresponding \verb|MATLAB|
codes are presented to effectively simulate the quantum circuits.
