On Nonuniform Noisy Decoding for LDPC Codes With Application to Radiation-Induced Errors

Recent studies on noisy decoding for LDPC codes rely on the assumption that the noise in each component is independent and perpetual. This paper examines a noisy decoding model that generalizes this approach: the noise is due to multi-state channels, where the channel states are governed by queue-like processes. This model is inspired by errors in decoders that are due to the high levels of radiation. This is an important problem, as modern non-volatile memories (NVMs) must perform well in high-radiation environments if they are to be used for deep space applications. High levels of radiation have a significant impact on floating gate-based NVMs, such as flash, and therefore, require well-tuned, powerful error-correcting codes for reliable data storage along with the decoders capable of handling radiation-induced noisy components. We introduce a noisy LDPC decoding model subsuming certain previously studied models. This model is better suited to represent transient errors-in both variable nodes and check nodes-and allows for a more refined analysis compared with older, coarser models. We perform a density evolution-like theoretical evaluation, applicable to both regular and irregular codes, optimize the voting threshold for a Gallager B/E-decoder, and analyze the resulting evaluation. We also examine the finite block length case.