Faster stochastic decoders for low density parity check codes

Abstract

The purpose of this thesis is to improve the convergence of stochastic belief propagation decoder for low-density parity-check (LDPC) codes. It is shown that belief propagation (BP) decoding approaches very closely the Shannon channel capacity when applied to LDPC codes with long block length. However, its hardware implementation is very complicated due to the randomness of the underlying code structure and the intensive probabilities computation used to detect and correct the eventual errors in transmission. This limitation hinders the wide applicability of LDPC codes in practical industrial systems compared to Turbo codes which are also known to achieve the Shannon capacity. A solution to this limitation was the use of the stochastic computation where the complex floating point circuits are replaced by simpler binary circuits operating over binary sequence representations of real entities. While the stochastic computation brings an elegant solution to the complexity of hardware implementation of the BP decoders, we aim to show in this work that there is room to improve its speed of convergence. In this context we propose two different methods intended to faster the convergence of stochastic decoders for LDPC codes. The first applies layering strategy to the stochastic decoder by modifying the schedule of the decoder updates. The simulation results show that there is an interesting gain in the average number of iterations to achieve a successful decoding; however, this solution suffers from a high error floor at high signal to noise ratio (SNR). The second, which is our main contribution, makes a decision to neglect the information from channel when a fixed number of a specific event is observed. Thorough testing reveals that this method provides almost the same convergence gain as the first one. Furthermore, it brings another important advantage: lowering the error floor; nevertheless, it does not modify the schedule of the decoder in contrast to the f...