It's highly recommended, stock kernel has lag issues. Made a quick search here for 4.3 touchwiz kernels, also, the last comments in AR HD surely talk about what kernels fits best the rom.
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I assume you have root a custom recovery like clockwork or teamwin. First flash your tw based rom. There are many kernels, like yank555, boeffla, adam, googy, it depends on you what you want: performance, batter, stability. When you choose what ke...
4.3 roms change the modem, and the efs format, so if you go back to 4.1 the modem cannot read your imei. Try flashing a 4.3 touchwiz based rom, like Android revolution, omega, s4 revolution rom. Just remember to flash a custom kernel too. Sorry fo...