Gallager B Decoder on Noisy Hardware

Abstract

Conventional communications theory assumes that the data transmission is noisy but the processing at the receiver is entirely error-free. Such assumptions may have to be revisited for advanced (silicon) technologies in which hardware failures are a major concern at the system-level. Hence, it is important to characterize the performance of a communication system with both noisy processing components and noisy data transmission. Coding systems based on low-density parity check (LDPC) codes are widely used for a variety of applications. In this paper, we focus on probabilistic analysis of the LDPC Gallager B decoder built out of faulty components. Using the density evolution technique, we find approximations for the optimal threshold of the decoder and the symbol error rate (SER) of the decoded sequence as functions of both the channel error rate and error rates of the decoder components, for both binary and non-binary regular LDPC codes. Furthermore, we study the convergence of the output SER and the decoding threshold of the decoder for different ranges of error rates. We verify our results using MATLAB simulations and hardware emulation of noisy decoders. Results presented in this paper can serve as systematic design guidelines in resource allocation for noisy decoders. Informed resource allocation is of particular relevance to emerging data storage and processing applications that need to maintain high levels of reliability despite hardware errors in advanced technologies.