Abstract :
Data rates on optical fibers are increasing at an astounding rate, with lab experiments reaching 100 trillions bits per second on a single fiber. To ensure the reliable transmission at such high data rates requires on the one hand increasingly sophisticated processing techniques and on the other hand puts severe constraints on the complexity of such algorithms. One important processing component is error correction coding. The intention of this workshop is to expose the audience to two fairly recent developments in coding theory which are both very well suited for optical communications — polar codes and spatially coupled codes. The program consists of two tutorials, explaining the basics of each of these coding schemes, followed by a talk which discusses hardware implementations. Polar codes were introduced in 2007 by Erdal Arikan. They represent a fundamentally new way of achieving capacity over a wide variety of channels with a low-complexity decoding algorithm. Their encoding and decoding structure is reminiscent of a Fast Fourier transform circuit, leading to efficient algorithms which take only N log(N) operations, where N is the block length. One of the many appealing features of polar codes is that their error performance can be tightly bounded analytically, hence eliminating the need for large scale simulations to explore in particular their error floor behavior. Spatially-coupled codes are constructed as follows. Start with a sparse graph code, e.g., an LDPC code. Replicate this code lets say L times (think of L=10) and place the replicas on a line. Connect neighboring replicas via edges. This spatial structure has the somewhat magical consequence that the threshold under the low complexity message-passing algorithm is essentially equal to the maximum-likelihood (ML) threshold (optimal decoding) of the underlying sparse graph code. Since for ML decoding it is very easy to construct codes with good thresholds and low error floors, this gives- - an entirely new way of constructing codes.
