How the UE goes out of sync in LTE?

The full procedure for determining if the link has failed due to being out of sync is shown in the figure below. There are 3 main parameters/timers involved:

n310: This parameter indicates the number of 200 ms intervals when the UE is unable to successfully decode the PDCCH due to low RSRP detected. That is, this parameter indicates the number of times in which the UE cannot successfully decode 20 consecutive frames in the downlink.

t310: It is a timer, in seconds, used to allow the UE to get back in synchronization with the eNodeB.

n311: This parameter indicates the number of 100 ms intervals that the UE must successfully decode the PDCCH to be back in-synch with the eNodeB. That is, this parameter indicates the number of times in which the UE must successfully decode 10 consecutive frames in the downlink in order for the UE to assume the radio link is in-synch.

If the UE detects n310 consecutive out-of-sync indications, it starts the t310 timer. If the timer expires, the link has failed. If the UE detects n311 consecutive in-sync indications prior to the t310 timer expiring, then the timer is stopped and the link has will not fail. 

RACH Preamble and Root Sequence Planning

The total number of RACH preambles available in LTE is 64. These preambles are shared among users for initial access and handover. Access to LTE systems can be classified based on the reservation or not of preambles for access. When users have a reserved signature to access the system, they are said to be using Contention Free Random Access (CFRA). On the contrary, when users don't have a reserved signature for access they are said to use Contention Based Random Access. CFRA is typically used during handover and  at the arrival of DL data. 

The 64 preambles are not implicitly communicated to the UEs by the eNodeB but rather, the UE is informed about the process of how to generate them via parameters broadcast in SIB2. These parameters are:
a)     RootConfigurationIndex
In LTE, there are 838 root Zadoff-Chu sequences available for preambles. The length of each root sequence is 839. RootConfigurationIndex, informs the UE via SIB2 which sequence is to be used.
b)    ZeroCorrelationZoneConfig.
One root sequence can generate several preambles by cyclic shift. One or more root sequences are needed to generate all preambles in a cell. The UE starts with the broadcasted root index and applies cyclic shifts to generate preambles. ZeroCorrelationZoneConfig points to a table where the cyclic shift is obtained from.
The smaller the cyclic shift, the more preambles can be generated from a root sequence. Hence, the number of sequences needed to generate the 64 preambles in a given cell is:
                        # of rows = ceiling (64 / (integer (sequence length/cyclic shift)))
For example, if the rootsequence index is 300 and the cyclic shift is 119, then, the number of rows needed to generate the 64 preambles in a cell is:
# of rows = ceiling(64 /(integer(839/119))) = 10
This means, that if we allocated rootsequenceindex 300 to cell X, then cell Y must have rootsequenceindex 310 and cell Z must have rootsequenceindex 320 to avoid root sequence conflict which might affect the RACH success rate of the cell.
Below is the mapping between NCS & Cell radius

Reference:http://lteuniversity.com/get_trained/expert_opinion1/b/lauroortigoza/archive/2011/10/20/rach-preamble-planning.aspx