Performance of polar codes for channel and source coding

Abstract

Polar codes, introduced recently by Arıkan, are the first family of codes known to achieve capacity of symmetric channels using a low complexity successive cancellation decoder. Although these codes, combined with successive cancellation, are optimal in this respect, their finite-length performance is not record breaking. We discuss several techniques through which their finite-length performance can be improved. We also study the performance of these codes in the context of source coding, both lossless and lossy, in the single-user context as well as for distributed applications.

Folded successive cancelation decoding of polar codes

“…A semi-parallel decoder was proposed in [6] as a simple architecture for resource sharing with a small increase in latency. Along the second line, to improve error performance, higher complexity decoders have been investigated such as list decoder in [7], belief propagation (BP) in [9], [8] and the sphere decoding based maximum likelihood (ML) decoders in [10], [11].…”

Enhanced Belief Propagation Polar Decoder for Finite Lengths

“…In [8] and [11], it is noted that the nodes in the factor graph of polar codes have a degree of two or three, while for LDPC codes, check nodes and variable nodes have an average degree of more than three. This is the reason why polar codes do not perform well at shorter lengths.…”

“…It is not only used for channel coding, but also in many other fields like computer vision, image processing, and medical research. It has been proved that the complexity of decoding polar codes under BP is  [6][7][8].…”

Polar coding for the Slepian-Wolf problem based on monotone chain rules

“…Polar coding for the above Slepian-Wolf problem was first considered by Hussami et al [2] (see also Korada [3]) who showed that the corner points of R SW could be achieved by polar codes for the special case where P X and P Y are uniform on {0, 1}. In [4], this result was proved without any restrictions on P X and P Y .…”

“…The decoder observes the two codewords and is expected to recover (X N , Y N ) with small probability of error. The Slepian-Wolf result [1] states that this is possible if (R 1 , R 2 ) falls strictly inside the Slepian-Wolf rate region defined asThe subset of R SW consisting of points for which R x + R y = H(X, Y ) is referred to as the dominant face (of the rate region); and the points (R x , R y ) = (H(X), H(Y |X)) and (R x , R y ) = (H(X|Y ), H(Y )) are referred to as the corner points.Polar coding for the above Slepian-Wolf problem was first considered by Hussami et al [2] (see also Korada [3]) who showed that the corner points of R SW could be achieved by polar codes for the special case where P X and P Y are uniform on {0, 1}. In [4], this result was proved without any restrictions on P X and P Y .…”