Efficient Algorithms for Stochastic Decoding of LDPC Codes

The expanding demand for high-speed communications has resulted in development of high-throughput error-correcting techniques required by emerging communication standards. Low-Density Parity-Check (LDPC) codes are a class of linear block codes that achieve near-capacity performance and have been selected as part of many digital communication standards. Stochastic computation has been proposed as a hardware efficient approach for decoding LDPC codes. Using stochastic computation, all messages in the iterative decoding process are represented by Bernoulli sequences. Computations on these sequences are performed bit-by-bit using simple logic operations. Furthermore, serial messages used in stochastic decoders help alleviate routing congestion in hardware implementation of decoder. These factors make stochastic decoding a low complexity alternative to implement LDPC decoders. In this dissertation, we analyze the characteristics of stochastic decoding and propose reduced-latency designs for stochastic LDPC decoders to achieve improved performance on various channel models.;We statistically analyze the behavior of stochastic LDPC decoding, including randomization in the stochastic streams and convergence of transition probabilities in iterative decoding process. We also present a space and time-efficient code bit determination method for stochastic LDPC decoders. In addition, we investigate and characterize the decoding errors of stochastic LDPC decoders and as an example, study the stochastic-decoding-specific trapping sets in the (1056,528) LDPC code used in the WiMAX standard. This study helps to develop methods to lower the error floor of stochastic decoding.;We propose a reduced-latency stochastic decoding algorithm for LDPC codes. The proposed algorithm, called Conditional Stochastic Decoding (CSD), improves error rate performance and reduces the decoding latency by more than 30% compared with the existing stochastic decoders. We also characterize the performance of CSD in various communication schemes. For example, we show the advantages of using the proposed CSD algorithm in the Automatic Repeat reQuest (ARQ) scheme when compared with other iterative decoding algorithms.;We extend our study of stochastic decoding to non-AWGN channel models including the Binary Symmetric Channel (BSC), the Z-channel, and the Rayleigh fading channel. We introduce scaling methods to improve the performance of stochastic decoding on these channel models. On the Rayleigh fading channel, the proposed method not only reduces the computational complexity of the stochastic decoding, but also provides 3-dB improvement in performance and lowers the error floor. Simplicity of hardware implementation, low latency, and good error rate performance of the proposed schemes make them suitable for emerging communication standards.