On Metric Sorting for Successive Cancellation List Decoding of Polar Codes

We focus on the metric sorter unit of successive cancellation list decoders for polar codes, which lies on the critical path in all current hardware implementations of the decoder. We review existing metric sorter architectures and we propose two new architectures that exploit the structure of the path metrics in a log-likelihood ratio based formulation of successive cancellation list decoding. Our synthesis results show that, for the list size of $L=32$, our first proposed sorter is $14\mathrm{\%}$ faster and $45\mathrm{\%}$ smaller than existing sorters, while for smaller list sizes, our second sorter has a higher delay in return for up to $36\mathrm{\%}$ reduction in the area.