Workshop on Modern Error Correcting Codes

Andrew R. Barron (Yale University)

Title: Sparse Superposition Codes: Adaptive Successive Decoding is Provably Fast and Reliable at all Rates R < C [Slide]

Abstract: While empirical methods have been found in the last 20 years to reliably communicate at high rates for practical real noise channels, theory of a practical scheme provable to have exponential error probability at any rate R < C has been lacking. Here we discuss recent developments establishing success of sparse superposition codes with iteratively optimal coefficient estimates interpretable as an adaptive successive decoding of code pieces. This is joint work with Antony Joseph and Sanghee Cho.

Kenta Kasai (Tokyo Institute of Technology)

Title: Spatially Coupled Codes [Slide]

Abstract: Spatially coupled codes have been observed to approach capacity for a variety of problems including memory channel coding, multi-user communication, quantum error correction, compressed sensing, and rate-less coding. The principle behind their excellent performance is analytically shown for the BEC that the BP threshold of a coupled ensemble converges to the maximum-a-posteriori (MAP) threshold of the uncoupled ensemble. This phenomenon is now called threshold saturation. In this talk, we introduce their definition, analytical tool, code design, universality, extension and applications.

Ryuhei Mori (Tokyo Institute of Technology)

Title: Introduction to Polar Codes [Slide]

Abstract: Polar codes are provably capacity achieving error-correcting codes with low encoding and decoding complexity for any discrete memoryless channel, discovered by Arikan in 2008. Here, basic properties of polar codes are discussed, e.g., the recursive structure, successive cancellation decoding, polarization phenomenon, rate of polarization, etc.