  Streaming codes represent a packet-level FEC scheme for achieving reliable,
low-latency communication. In the literature on streaming codes, the
commonly-assumed Gilbert-Elliott channel model, is replaced by a more
tractable, delay-constrained, sliding-window (DCSW) channel model that can
introduce either random or burst erasures. The known streaming codes that are
rate optimal over the DCSW channel model are constructed by diagonally
embedding a scalar block code across successive packets. These code
constructions have field size that is quadratic in the delay parameter $\tau$
and have a somewhat complex structure with an involved decoding procedure. This
led to the introduction of simple streaming (SS) codes in which diagonal
embedding is replaced by staggered-diagonal embedding (SDE). The SDE approach
reduces the impact of a burst of erasures and makes it possible to construct
near-rate-optimal streaming codes using Maximum Distance Separable (MDS) code
having linear field size. The present paper takes this development one step
further, by retaining the staggered-diagonal feature, but permitting the
placement of more than one code symbol from a given scalar codeword within each
packet. These generalized, simple streaming codes allow us to improve upon the
rate of SS codes, while retaining the simplicity of working with MDS codes. We
characterize the maximum code rate of streaming codes under a constraint on the
number of contiguous packets over which symbols of the underlying scalar code
are dispersed. Such a constraint leads to simplified code construction and
reduced-complexity decoding.
