  Currently, there are mainly three kinds of Transformer encoder based
streaming End to End (E2E) Automatic Speech Recognition (ASR) approaches,
namely time-restricted methods, chunk-wise methods, and memory-based methods.
Generally, all of them have limitations in aspects of linear computational
complexity, global context modeling, and parallel training. In this work, we
aim to build a model to take all these three advantages for streaming
Transformer ASR. Particularly, we propose a shifted chunk mechanism for the
chunk-wise Transformer which provides cross-chunk connections between chunks.
Therefore, the global context modeling ability of chunk-wise models can be
significantly enhanced while all the original merits inherited. We integrate
this scheme with the chunk-wise Transformer and Conformer, and identify them as
SChunk-Transformer and SChunk-Conformer, respectively. Experiments on AISHELL-1
show that the SChunk-Transformer and SChunk-Conformer can respectively achieve
CER 6.43% and 5.77%. And the linear complexity makes them possible to train
with large batches and infer more efficiently. Our models can significantly
outperform their conventional chunk-wise counterparts, while being competitive,
with only 0.22 absolute CER drop, when compared with U2 which has quadratic
complexity. A better CER can be achieved if compared with existing chunk-wise
or memory-based methods, such as HS-DACS and MMA. Code is released.
