How to convert gapless m4a tracks into a gapless HLS stream - avplayer

Question

I have an album stored as a list of gapless m4a files, ripped from CD. I need to stream the album gaplessly over HTTP Live Streaming, and the user must be able to "jump in" at the start of any track. For now, my only client is AVPlayer on iOS.
I can segment the tracks individually using Apple's mediafilesegmenter tool. For each track, this produces one .m3u8 playlist file and several .aac segment files, each ~10 seconds in duration except for the last.
The m3u8 playlist for Track 1 looks like this:
#EXTM3U
#EXT-X-TARGETDURATION:11
#EXT-X-VERSION:3
#EXT-X-MEDIA-SEQUENCE:0
#EXT-X-PLAYLIST-TYPE:VOD
#EXTINF:10.001,
segment0.aac
#EXTINF:9.983,
segment1.aac
...
#EXTINF:3.231,
segment23.aac
#EXT-X-ENDLIST
I can combine these m3u8 playlist files into one master m3u8 file for the album:
#EXTM3U
#EXT-X-TARGETDURATION:11
#EXT-X-VERSION:3
#EXT-X-MEDIA-SEQUENCE:0
#EXT-X-PLAYLIST-TYPE:VOD
#EXTINF:10.001, // begin track 1
segment0.aac
#EXTINF:9.983,
segment1.aac
...
#EXTINF:3.231,
segment23.aac
#EXT-X-DISCONTINUITY
#EXTINF:10.001, // begin track 2
segment24.aac
#EXTINF:9.983,
segment25.aac
...
#EXTINF:6.845,
segment46.aac
#EXT-X-DISCONTINUITY
#EXTINF:10.001, // begin track 3
segment47.aac
#EXTINF:9.983,
segment48.aac
...
#EXTINF:8.012,
segment80.aac
#EXT-X-ENDLIST
It will play through the whole album, but it isn't gapless. Notice the DISCONTINUITY tag between each track (without it, the player hangs forever). This introduces a small gap between tracks, maybe 300 milliseconds.
How can I create segments that flow into each other with no discontinuity?

Answer 1

You can concatenate the AAC files before using the mediafilesegmenter tool on the combined AAC file.
The following ffmpeg command might generate the output file.
ffmpeg -i "concat:input1.aac|input2.aac|input3.aac" -c copy output.aac
It's possible you'll need to remux the aac files to mpeg2ts files before concatenation, and then remux the mpeg2ts file to AAC.