k. The complete process is depicted in Figure 3.11. 3.2.4 Coding Techniques in LTE Two different coding techniques have been chosen for channel coding in LTE: tail biting convolutional coding for control channels and turbo coding for data chan- nels. The final bit sequence obtained as a result of the coding processes is referred to as a coded block. 3.2.4.1 Tail Biting Convolutional Coding Convolutional codes, first introduced in Elias (1954, 29), allow for achieving a coding rate of 1/m because a set of m coded bits (dio d(m-1)) is generated for each input bit, Ck. Resulting coded bits depend on both the current bit and a number of previous bits determined for the constraint length, k, of the encoder. In LTE, control channels are coded with a tail biting convolutional code with a coding rate 1/3 and a constraint length of 7, as depicted in Figure 3.12. At the receiver end, a decoding process is requested to recover the original sequence of data bits. This process is usually based on the Viterbi algorithm (Viterbi © 2009 by Taylor & Francis Group, LLC Radio-Interface Physical Layer Information bits Coded Figure 3.12 Tail biting convolutional coding scheme. 1967, 260), which has the advantage of performing the maximum likelihood decod- ing. Additionally, the Viterbi algorithm is highly parallelizable and therefore ideal for hardware decoder implementation. 3.2.4.2 Turbo Coding Turbo codes, first proposed by Berrou, Glavieux, and Thitimajshima (1993, 1064), enable reliable communications with efficiencies close to the theoretical limit pre- dicted by Shannon (1948,379). Since their introduction, turbo codes have been proposed for low-power systems (e.g., satellite communications or interference lim- ited scenarios like third-generation cellular technology). LTE turbo encoding is based on two eight-state constituent encoders and one turbo code internal interleaver. The sequence of original input bits, Ck' is encoded by the first encoder; the input to the second encoder is an interleaved version of the original seque