[Galaxy S 4 General] jqm_:
I'm not a dev. All credits to OPs and devs colaborators.

Simply I make an updated index to our device.

If I make anything wrong, please, fix or delete thread.

Information:

There are three distinct versions of the Samsung Galaxy S4 LTE; Galaxy S4 LTE-A SK (SHV-E330S, ks01lteskt), Galaxy S4 LTE-A KT (SHV-E330K, ks01ltektt) and Galaxy S4 LTE + International (GT-I9506, ks01lte). The ROMs/kernels are NOT cross-compatible (unless otherwise stated in the respective threads).

The Samsung Galaxy S4 LTE models are more similar to the Samsung Galaxy Note 3's hardware than any of the other S4 variants (i9500, i9505, i9505G), but unfortunately they are still not compatible with Note 3 ROMs/kernels

GSM Arena Specs [i9506 Galaxy S4] - LINK

SAMMOBILE latest news for the i9506 - LINK

(Copied from official index, by DahakePL)

##TOOLS

ODIN 3 - LINK

##USEFUL FILES

GT-i9506 MODEM Colection Thread by hr2 LINK

PIT file, by xenix96 LINK

*xposed causes bootloop in stock rom/odexed roms. Use deodexed touchwiz baseds or aosp/cm baseds.

[OFFICIAL] Xposed framework Thread by revo89 LINK

Xposed framework (5.0.x) LINK

Xposed framework (5.1.x) LINK

Xposed framework (6.0.x) LINK

Xposed installer apk LINK

Xposed uninstaller LINK

(many aosp/cm roms have problems with default musicfx. I recomend this)

ViPER4Android Thread by IAM_TheFlash LINK

##RECOVERIES

[OFFICIAL] TWRP 3.0.2-0 LINK (more recommend)

[ks01lte] TWRP 3.0.2-0 touch recovery with F2FS support [2016-05-08] Thread by CastagnaIT LINK

[UNOFFICIAL]ClockWorkMod Recovery 6.0.4.6 for i9506 Thread by dridri85 LINK

6.0.5.1 ClockworkMod recovery] sd-ext working Thread by konsolen LINK

PhilZ touch 6.59.0 (ks01lte), by xxchrisxx LINK

##KERNELS

ONjA kernel for Galaxy S4 LTE-A GT-I9506 Thread by ONjA LINK

arter97 kernel for Galaxy S4 LTE-A Thread by arter97 LINK

stock official releases

GT-i9506 (ks01ltexx) LINK

SHV-E330K (ks01ltett)LINK

SHV-E330L (ks01ltegt)LINK

SHV-E330S (ks01ltekt)LINK

GT-i9506 [5.0.1] download via MEGA by DeHAWK LINK

##ROMS

Stock baseds

[5.0.1] Pre-Rooted 5.0.1 OC/NON-OC kernel - Full/Slim De-Odexed ROM. Thread by DeHAWK LINK

[5.0.1][E330SKL/I9506] JuMBO v1.0 | Deodexed | Deknoxed | Stable | Thread by BarakOsama LINK

[5.0.1][E330][19-JUL]★D.A Rom™ V2.1★FAST-SLIM-DEODEXED✄STABLE✄ Thread by pereradileepa LINK

[5.0.1][DOH2] Truongtan S4 Portable Fast and Smooth (Updated 20.11.2015) Thread by tanthuychivietnam LINK

[5.0.1]NEE LRX22C.I9506XXUDOF2 @ JX!2015 5.0.1 StockRom - Preroot - Zipalign - Deo-xed Thread by Jerome-X LINK

[5.0.1][i9506][LP][eXtremely Tweaked][De-bloated] Thread by t-shock LINK

[5.0.1][MilkyWay.ROM @ JX!2015 | 5.0.1 Preroot - Zipalign - Deo-xed - Slim -Fast -Clean Thread by Jerome-X LINK

[5.0.1]DTM LRX22C.I9506XXUDOF2 @ JX!2015 5.0.1 StockRom - Preroot - Zipalign - Deo-xed Thread by Jerome-X LINK

Towchwiz based/ports

//KITKAT 4.4x

[4.4.x][I9506] [S5] TouchWizz v5 2.1 Stable Thread by Developer.WL LINK

//LOLLIPOP 5.0.x

[5.x.x][i9506][port][stable]AryaMod V8.3 TW Lollipop Thread by 3lambda LINK

[5.0.x]Qaraqumus [12.06 .16] [5.0] [XXUGBPD3] qs-9005-lp [Note 3 port] Thread by same-xx LINK

[5.0.x][S6 Port]Norma Rom S6 V15[Fast and Stable][ABANDONED] Thread by DahakePL LINK

[5.0.x][ABANDONED][i9506][PORT][LP] Note 4 firmware for Galaxy S4 LTE-A Thread by t-shock LINK

[5.0.x]Galaxy S5 firmware for Galaxy S4 LTE-A Thread by arter97 LINK

[5.0.1]Truongtan s5 rom for e330slk/i9506 - fast and smootth rom(version 11.0.1) Thread by tanthuychivietnam LINK

[5.0.1][Note 4 Full port][01.09.2015]AuroraRom Note 4 V6 Thread by DahakePL LINK

[5.0.1]Truongtan note4 stable for e330slk/i9506 _ fast and smooth Thread by tanthuychivietnam LINK

[5.0.1]JeSuisParis.ROM @ JX! | 5.0.1 Preroot - Zipalign - Deoxed - Slim -Fast -Clean Thread by Jerome-X LINK1

[5.0.1]SUNSHINE ROM V5.0.1 for E330 S L K / i9506 (V6.0 On the Way) Thread by malinga119 LINK

[5.0.1]Truongtan dol4 rom v1.0.1 for e330slk/i9506 Thread by tanthuychivietnam LINK

[5.0.2][16-08-15][GT-I9506][PORT] Darklord Galaxy S6 v3.0 for S4 Thread by Dexter_nlb LINK

[5.0.2]s6 stable rom for e330slk/i9506 Thread by tanthuychivietnam LINK

[5.0.2]DarkLord S6 Alpha [10/05/2015] Thread by t-shock LINK

[5.0.2]DarkLord S6 port for Galaxy S4 LTE-A Thread by arter97 hLINK

//LOLLIPOP 5.1.x

[5.1.1][S6 Port]Truongtan Sunshine V10.0.1 for E330SLK/I9506[Link updated 24/11/2015] Thread by tanthuychivietnam LINK

[5.1.1][Port][N5 Port][05.05.2016] Phronesis Rom v6.5 Feature Rich Thread by DahakePL LINK

[5.1.1][N5 Port]Truongtan Note 5 Rom For E330SLK/I9506 ( updated link 04.11.15) Thread by tanthuychivietnam LINK

//MARSHMALLOW 6.0.1

[6.0.1][V4.4.1][PORT] S5 TouchWiz Marshmallow for galaxy S4 advance Thread by 3lambda LINK

[6.0.1][Aroma][OTA]AryaMod Port S7Edge PortV6.2 [Final][04 July 2016] Thread by 3lambda LINK

[6.0.1][DarkWolf_FW][Galaxy S7 Edge Port][V2][20/04/2016][Super fast]ON-LINE! Thread by DahakePL LINK

[6.0.1]TRUONGTAN S7 EDGE/NOTE UX ROM FOR S4 E330SLK-I9506 Thread by tanthuychivietnam LINK

[6.0.1][UPDATE 12/5/2016] S7 EDGE ROM V6 FOR S4 E330SLK/I9506 Thread by tanthuychivietnam LINK

[6.0.1][V4.1][PORT] S5 TouchWiz Marshmallow for S4 LTE-A Thread by cedric3 LINK

[6.0.1]touchwiz Rom for s4 i9506 Thread by arbers4 LINK

AOSP/CyanogenMod baseds/anothers ports

//KITKAT 4.4.x

[4.4.x]Unofficial build of CyanogenMod 11.0 for GT-I9506 Thread by NeuDLi LINK

[4.4.x]CyanogenMod 11.0 for Galaxy S4 LTE-A (GT-I9506) Thread by solk2 LINK

[4.4.4]Unofficial build of CyanogenMod 11.0 for GT-I9506 Thread by NeuDLi LINK

[4.4.4][CM11.0] MIUI V5 for I9506 Thread by leeweijie99 LINK

[4.4.4][Unofficial] Carbon Rom 4.4.4 based on CM11.0 [30.06.14] Thread by a2441918 LINK

[4.4.4]SPL(Gaming)[Official] 03/01/2015 Thread by Buda1996 LINK

[4.4.4][ks01lte][UNOFFICIAL] Daydream 1.8 KK 4.4.4 Thread by Genie's LINK

//LOLLIPOP 5.0.x

[5.0.x]SPL(Gaming)[Official] 03.01.2015 Thread by Buda1996 LINK

[5.0.x]CyanogenMod 12 (Android 5.0 Lollipop) for Galaxy S4 LTE-A Thread by arter97 LINK

[5.0.x]SPL[Meta-OS] 23.May.2015(TestBuild) Thread by Spike-Lab LINK

[5.0.x][ks01lte][Unofficial] AICP. Android Ice Cold Project by jonte28 LINK

[5.0.2][SlimLP Unofficial] Thread by a2441918 LINK

//LOLLIPOP 5.1.x

[5.1.1][5.1.6.6R]MeiZu's Flyme OS 5 by Wonitor (S4) Thread by karkasss LINK

[5.1.1]flyme os 4.5.4 r2 android 5.1.1 multilanguaje Thread by luistro LINK

[5.1.1]SkulptorRom @ JX!2015 | 5.1.1 | Slim -Fast -Clean | Thread by Jerome-X LINK

[5.1.1][unofficial][Lollipop 5.1.1][ks01lte]PAC-ROM LP-MR1 Thread by Backstrom98 LINK

[5.1.1]CyanogenMod 12.1 for Galaxy S4 LTE-A (GT-I9506) Thread by solk2 LINK

[5.1.x]CyanogenMod 12.1 (Android 5.1) for Galaxy S4 LTE-A Thread by arter97 LINK

[5.1.x][GT-I9506] "Metallium ROM" by Spike Lab Thread by Buda1996 LINK

//MARSHMALLOW 6.0.1

[6.0.1][ROM][5.1.1-6.0.1][AOSP] Official Mokee for KS01LTE Thread by 3lambda LINK

[6.0.1]CyanogenMod 13.0 for Galaxy S4 LTE-A (GT-I9506) Thread by solk2 LINK

[6.0.1][ks01lte] RESURRECTION REMIX M [5.7.4][CM13][unofficial I9506][20.09.16] Thread by Eliminater LINK

[6.0.1]Resurection remix 5.6.7 Unofficial Thread by 3lambda LINK

[6.0.1][I9506] Dirty Unicorns v10.6 [Dirty-Deeds][CAF][11.09.16] Thread by Eliminater LINK

[6.0.1][ks01lte] Temasek's UNOFFICIAL CyanogenMod 13 Thread by arter97 LINK

[6.0.1]CandySiX [3.2][I9506][KS01LTE][6.0.1] 04.09.2016 Thread by Eliminater LINK

[6.0.1][21.05.2016][ROM][ks01lte] AICP MM 11.0 UNOFFICIAL [I9506][cm13] Thread by Eliminater LINK

[6.0.1/5.1.1] Unofficial Temasek Builds cm13/12.1 Thread by trader418 LINK

[6.0.1][GT-I9506][ks01lte] CyanogenMod 13.0 UNOFFICIAL for the Galaxy S4 LTE-A Thread by kyasu LINK

[6.0.1/5.1.1]Stable CyanogenMod 12.1/13.0 for Galaxy S4 LTE-A Thread by arter97 LINK

[6.0.1][ks01lte] ValidusOs-M by GZR [AOSP+CMTE+DUI][Great Experience] Thread by Eliminater LINK

[6.0.1][i9506] PAC MAN ROM [M][CM][KS01LTE][30.07.16] Thread by Eliminater LINK

[6.0.1][v6.17] Beanstalk I9506 ks01lt[UNOFFICIAL][Great Experience][DU-Features] Thread by Eliminater LINK

[6.0.1][UNOFFICIAL] Slim6 Marshmallow [I9506][ks01lte] Thread by Eliminater LINK

[6.0.1][I9506][BlissROM] [V6.4][ks01lte][UNOFFICIAL] Thread by Eliminater LINK

[6.0.1][MARSHMALLOW]BLUROS 6.0.1 FOR KST01 E330SLK/I9506 Thread by tanthuychivietnam LINK

[6.0.1][ks01lte] UNOFFICIAL AICP Thread by Backstrom98 LINK

Don't forget hit thanks/donate to devs/supporters.