Least reliable messages based early termination method for LT soft decoder

In this paper, we propose a new early termination method (ETM) for Luby transform (LT) belief propagation (BP) decoder. The proposed ETM, which we call least reliable messages (LRM), observes only sign alterations of a small cluster in log-likelihood ratio (LLR) messages passing between nodes in BP decoder. Simulation results and complexity analyzes show that LRM significantly lower computational complexity of early termination section in decoder without any performance degradation and decreases the average decoding iteration amounts compared to conventional ETMs in literature. The method can be easily applied to code families which can be decoded by BP such as low density parity check (LDPC) codes, polar codes and Raptor codes. Introduction: Due to their capacity-approaching and unique rateless properties, there has been a particular interest in using Luby transform (LT) and Raptor codes, which are members of rateless codes family, over noisy channels [1, 2]. Message-passing algorithms such as belief propagation (BP) are used for decoding of rateless codes. BP iterative decoder uses a pre-set fixed iteration number in order to stop decoding. However, BP mostly converges to original data at an early stage of decoding. Since the decoding continues up to pre-set fixed iteration number, decoder performs redundant processes which cause high computational complexity, decoding latency and energy dissipation. To avoid the aforementioned negations, decoder should be supported by an early termination mechanism to detect convergence and stop decoding. In literature, there are some early termination methods (ETMs) based on check-sum satisfaction ratio (CSR) for rateless codes [3]-[6]. CSR is a common success criterion for BP decoding algorithm to observe whether message estimation satisfies constraints imposed by check nodes. Iterative BP decoding algorithm is performed through log-likelihood ratio (LLR) message-passing between nodes. At the end of each iteration CSR decides output bits, re-encodes them and compare with input bits to determine successful convergence. In this letter we propose a completely new ETM for LT BP decoder which we denote as least reliable messages (LRM) ETM. Our method observes only sign alterations of a small cluster in passing LLR messages between BP nodes. Results show that proposed LRM ETM significantly reduces the computational complexity of early termination section in decoder without any performance loss and also decreases the average iteration amounts compared to CSR.