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Springer eBooks

Stochastic Decoders for LDPC Codes

François Leduc-Primeau, Vincent Gaudet, Warren J. Gross

Published Oct 17, 2014• 2 citations
Publisher
DOI
10.1007/978-3-319-10569-7_6

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This letter presents the first successful method for iterative stochastic decoding of state-of-the-art low-density parity-check (LDPC) codes. The proposed method shows the viability of the stochastic approach for decoding LDPC codes on factor graphs. In addition, simulation results for a 200 and a 1024 length LDPC code demonstrate the near-optimal performance of this method with respect to sum-product decoding. The proposed method has a significant potential for high-throughput and/or low complexity iterative decoding.
A new stochastic decoding algorithm, called Delayed Stochastic (DS) decoding, is introduced to implement low-density-parity-check (LDPC) decoders. The delayed stochastic decoding uses an alternative method to track probability values, which results in reduction of hardware complexity and memory requirement of the stochastic decoders. It is therefore suitable for fully-parallel implementation of long LDPC codes with applications in optical communications. Two decoders are implemented using the DS algorithm for medium (2048, 1723) and long (32768, 26624) LDPC codes. The decoders occupy 3.93- mm2and 56.5- mm2silicon area using 90-nm CMOS technology and provide maximum core throughputs of 172.4 and 477.7 Gb/s at [(Eb)/(No)]=5.5 and 4.8 dB, respectively.
Stochastic decoding is a hardware and energy-efficient approach to implement iterative Low-Density Parity-Check (LDPC) decoders. However, stochastic decoding often has a performance loss compared to the sum-product algorithm and suffers from additional trapping sets, which limit the performance of LDPC codes in the error floor region. In this paper, we investigate the error characteristics of stochastic LDPC decoding. We also report stochastic-decoding-specific trapping sets for the (1056,528) LDPC code from the WiMAX standard. This observation has a potential to guide code structure designs that lower the error floor in stochastic decoding.