How would one classify a stream cipher that is neither synchronous, nor self synchronizing? I would have thought asynchronous, but from all the sources I can find, asynchronous is synonymous with self synchronizing.
The internal state of the cipher is initialized by a key and initialization vector. The internal state is modified depending on the current internal state, and the previous byte of plain text. The cipher does not synchronize after a fixed number of bytes. Error propagation is unlimited, so corruption of one byte of cipher text makes the rest of the message undecipherable.
I would like to know the correct classification of the cipher.
Thanks to @otis and @kodlu, who suggested the terms synchronous and additive. Searching those terms has led me to this article, describing nearly exactly what I am after. On page 244, I paraphrase, where W [...] is the running key sequence and where we allow W, to depend both on the secret key (as is customary) and on [all prior bytes of] the plaintext. This article is heavy on the maths and terms, so many of which I need to look up to understand their meaning. I am still working through the terms used in the article, which is why I have not proposed an answer to my own question. I am posting this source, because it might be helpful to someone with a stronger background to answer the question.