he hard-decision output based on the observed channel output yN and the previously decoded bits, for example, the kth decision element would compute ûk using y and -1 The decision element computes the likelihood ratio as follows [29]: The hard decision per decision element is generated according to the following rule: The decision elements of indices that belong to the set Ac are set to zero ûk = 0, that is, frozen bit positions and values can be considered as the decoder's prior knowledge. 522 Chapter 4 In the SC decoding process, the value selected for each bit in the recovered information block depends on the sign of the corresponding LLR, which in turn depends on the values selected for all previous recovered information bits. If this approach results in the selection of the incorrect value for a particular bit, then this will often result in propagation of errors in all subsequent bits. The selection of an incorrect value for an information bit may be detected with consideration of the subsequent frozen bits, since the decoder knows that these bits should have zero values. More specifically, if the corresponding LLR has a sign that would imply a value of "1" for a frozen bit, then this suggests that an error may have occurred during the decoding of one of the preceding information bits. However, in the SC decoding process, there is no opportunity to consider alternative values for the preceding information bits. Once a value has been selected for an information bit, the SC decoding process is final. This motivates SCL decoding, which enables a list of alternative values for the information bits to be considered. As the decoding process continues, it considers both options for the value of each successive information bit. More specifically, an SCL decoder maintains a list of candidate kernel information blocks, where the list and the kernel infor- mation blocks are built up as the SCL decoding process proceeds. At the start of the pro- cess, the list comprises only a single-kernel information block having a l