2 research outputs found
List Decoding of Arikan's PAC Codes
Polar coding gives rise to the first explicit family of codes that provably
achieve capacity with efficient encoding and decoding for a wide range of
channels. However, its performance at short block lengths is far from optimal.
Arikan has recently presented a new polar coding scheme, which he called
polarization-adjusted convolutional (PAC) codes. Such PAC codes provide
dramatic improvement in performance as compared to both standard
successive-cancellation decoding as well as CRC-aided list decoding. Arikan's
PAC codes are based primarily upon the following ideas: replacing CRC precoding
with convolutional precoding (under appropriate rate profiling) and replacing
list decoding by sequential decoding. His simulations show that PAC codes,
resulting from the combination of these ideas, are close to finite-length
bounds on the performance of any code under ML decoding.
One of our main goals in this paper is to answer the following question: is
sequential decoding essential for the superior performance of PAC codes? We
show that similar performance can be achieved using list decoding when the list
size is moderately large (say, ). List decoding has distinct
advantages over sequential decoding is certain scenarios, such as low-SNR
regimes or situations where the worst-case complexity/latency is the primary
constraint. Another objective is to provide some insights into the remarkable
performance of PAC codes. We first observe that both sequential decoding and
list decoding of PAC codes closely match ML decoding thereof. We then estimate
the number of low weight codewords in PAC codes, using these estimates to
approximate the union bound on their performance under ML decoding. These
results indicate that PAC codes are superior to both polar codes and
Reed-Muller codes, and suggest that the goal of rate-profiling may be to
optimize the weight distribution at low weights.Comment: 9 pages, 10 figures, abridged version of this paper will be presented
at the International Symposium on Information Theory, June 202