Bits in a received word that is based on a codeword of a polar code are decoded to generate decoded bits. A lower-order partial sum is updated based on the decoded bits, and a higher-order partial sum based on the lower-order partial sum is computed. The higher-order partial sum computation is a live computation performed during decoding of a subsequent bit in the received word in some embodiments. In decoding the subsequent bit, nodes in a Data Dependency Graph (DDG) of the polar code may be traversed in a reverse order relative to node indices of at least some of the nodes in the DDG. A reverse order may also be applied to partial sum computations, to combine multiple lower-order partial sums that are based on previously decoded bits according to a reverse order relative to an order in which at least some of the previously decoded bits were decoded.