MIMO Decoding: SC vs SCL Algorithm Comparison

In the following text, we will conduct a comparative analysis of the SC (Successive Cancellation) and SCL (Successive Cancellation List) algorithms used in MIMO decoding systems.

The SC algorithm is a sequential decoding approach that processes bits in a predetermined order. In implementation, it typically employs a recursive tree structure where each node represents a likelihood ratio calculation. The algorithm propagates likelihood values from leaf nodes to the root, making hard decisions at each step without maintaining multiple candidate paths. This greedy approach can be implemented using binary tree traversal with complexity O(N log N), where N is the block length.

In contrast, the SCL algorithm maintains multiple candidate paths simultaneously during the decoding process. The key implementation aspect involves managing a list of L most promising paths, where L represents the list size parameter. At each decoding step, the algorithm extends all current paths, calculates path metrics using likelihood ratios, and prunes the list to retain only the L best-performing paths. This requires additional memory allocation for path storage and metric comparison operations.

Through comparison of these two algorithms, we can identify their distinct advantages and limitations. The SC algorithm demonstrates better performance with large datasets due to its lower computational complexity O(N log N) and minimal memory requirements. However, the SCL algorithm, while more computationally intensive with complexity O(LN log N), provides superior error correction performance by maintaining multiple hypotheses, particularly beneficial when dealing with labeled datasets where it can leverage additional information for more accurate grouping decisions. Therefore, algorithm selection should be determined based on specific dataset characteristics, performance requirements, and available computational resources.