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 i...
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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 gallagerb 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.
In this letter, we study the performance of a noisy gallagerb decoder used to decode irregular low-density parity-check (LDPC) codes. We derive the final bit error rate (bER) as a function of both the transmission no...
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In this letter, we study the performance of a noisy gallagerb decoder used to decode irregular low-density parity-check (LDPC) codes. We derive the final bit error rate (bER) as a function of both the transmission noise and processing errors. We allow different components of the decoder associated with certain computational units (i.e., bit and check nodes of varying degrees) to have different processing errors. We formulate an optimization problem to distribute available processing resources across different components of a noisy decoder to achieve minimal bER. Simulations demonstrate that the optimal resource allocation derived from our analysis outperforms uninformed (random) resource assignment.
binary message passing decoders for low-density parity-check codes are studied by using extrinsic information transfer charts. The channel delivers hard or soft decisions and the variable node decoder performs all com...
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binary message passing decoders for low-density parity-check codes are studied by using extrinsic information transfer charts. The channel delivers hard or soft decisions and the variable node decoder performs all computations in the log-likelihood ratio ( L-value) domain. A hard decision results in the gallager b algorithm and examples show that increasing the channel output alphabet to two bits gains more than 1.0 db in signal to noise ratio when using optimized codes. Finally, it is shown that errors on cycles consisting only of degree two and three variable nodes cannot be corrected and a necessary and sufficient condition for the existence of a cycle-free subgraph is derived.
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