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I found this in information theory paper, P.3883*

the authors states the following

Most existing theoretic studies of network coding focus on DAGs due to its simpler structure and dure to the fact that one can always convert a cyclic network to its acyclic counterpart by taking into account the time index and the causality of information transmission. Nonetheless, when studying Pair Intersession Network Coding on a cyclic network, one cannot rely on this cyclic-to-acyclic conversion since after conversion, there are T symbols in the $(s_1, d_1)$ (resp. $(s_2,d_2)$) multicast session and network coding allows complete freedom of mixing the $2T$ symbols $[X]_1^T$ and $[Y]_1^T$.

It looks ambiguity because does it mean that we have input from 1 to T; or Is it field = T and size = 1 (since capacity = 1)? so I hope I find answer here.

Thank you ..

*for those who doesn't have access go to this site Paper


Responsing to D.W. (The following information is for reference about the paper.)

C-C. Wang and N. B. Shroff. Pairwise Intersession Network Coding on Directed Networks. IEEE Tran. on Info. Theo., Vol. 56, No. 8, August 2010.

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This notation is quite common in EE works: If $S=S_1S_2S_3\cdots$ is a string (of some length), then

$S_i^j$ is the substring between places $i$ and $j$, that is, $S_i^j=S_i\cdots S_j$.

I didn't looks at the paper, but I guess that $[X]$ is a string (of expectations? of $X$ directly? this should be defined in the paper), and they just look at a prefix of length $T$ of that string.

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