Spatially coupled sparse codes on graphs: theory and practice

Since the discovery of turbo codes 20 years ago and the subsequent rediscovery of low-density parity check codes a few years later, the field of channel coding has experienced a number of major advances. Until that time, code designers were usually happy with performance that came within a few decibels of the Shannon Limit, primarily due to implementation complexity constraints, whereas the new coding techniques now allow performance within a small fraction of a decibel of capacity with modest encoding and decoding complexity. Due to these significant improvements, coding standards in applications as varied as wireless mobile transmission, satellite TV, and deep space communication are being updated to incorporate the new techniques. In this article, we review a particularly exciting new class of low-density parity check codes called spatially coupled codes, which promise excellent performance over a broad range of channel conditions and decoded error rate requirements.