Windowed Decoding of Spatially Coupled Codes

TL;DR

This paper analyzes a windowed decoding scheme for spatially coupled codes over erasure channels, showing it approaches belief propagation performance with reduced complexity and latency, supported by analytical bounds and numerical results.

Contribution

It introduces a windowed decoding approach for spatially coupled codes, providing analytical thresholds and demonstrating near-BP performance with smaller window sizes.

Findings

Thresholds approach belief propagation exponentially fast with window size

Analytical lower bounds on erasure thresholds are derived

Numerical results confirm the effectiveness of windowed decoding

Abstract

Spatially coupled codes have been of interest recently owing to their superior performance over memoryless binary-input channels. The performance is good both asymptotically, since the belief propagation thresholds approach capacity, as well as for finite lengths, since degree-2 variables that result in high error floors can be completely avoided. However, to realize the promised good performance, one needs large blocklengths. This in turn implies a large latency and decoding complexity. For the memoryless binary erasure channel, we consider the decoding of spatially coupled codes through a windowed decoder that aims to retain many of the attractive features of belief propagation, while trying to reduce complexity further. We characterize the performance of this scheme by defining thresholds on channel erasure rates that guarantee a target erasure rate. We give analytical lower bounds on these thresholds and show that the performance approaches that of belief propagation exponentially fast in the window size. We give numerical results including the thresholds computed using density evolution and the erasure rate curves for finite-length spatially coupled codes.