Schedule is the order of passing messages between vertices of the bipartite graph defining an LDPC code during decoding. Schedules may significantly differ in the rate of decoding convergence. New efficient generalized serial schedules are described and analyzed. They provide significant convergence rate speedup factors compared to previously known schedules. For the proposed schedules, combinatorial and probabilistic analysis is presented, explaining the fast convergence observed in simulations. Using it, LDPC ensembles for which significantly better convergence rates can be obtained are identified.
Schedule is the order of passing messages between vertices of the bipartite graph defining an LDPC code during decoding. Schedules may significantly differ in the rate of decoding convergence. New efficient generalized serial schedules are described and analyzed. They provide significant convergence rate speedup factors compared to previously known schedules. For the proposed schedules, combinatorial and probabilistic analysis is presented, explaining the fast convergence observed in simulations. Using it, LDPC ensembles for which significantly better convergence rates can be obtained are identified.
Schedule is the order of passing messages between vertices of the bipartite graph defining an LDPC code in the process of decoding. Schedules affect the rate of decoding convergence. New efficient generalized serial schedules are described and analyzed, exhibiting significantly faster convergence compared to previously known schedules. For the proposed schedules, combinatorial and probabilistic analysis is presented, explaining the fast convergence observed in simulations. Using it, LDPC ensembles for which significantly better convergence rates can be achieved are identified. Specific code constructions from lifted graphs are further proposed, efficiently supporting the schedules. Examples based on regular LDPC codes are provided, in which the schedules achieve convergence speedup factors of up to 6 in comparison with the flooding schedule. Higher speedup factors are predicted by the analysis for irregular codes.
Serial decoding schedules for low-density parity-check (LDPC) codes are described and analyzed. Conventionally, in each iteration all the variable nodes and subsequently all the check nodes send messages to their neighbors (“flooding schedule”). In contrast, in the considered methods, the updating of the nodes is implemented according to a serial schedule. The evolution of the decoding algorithm’s computation tree under serial scheduling is analyzed. The analysis shows that it grows twice as fast in comparison to the flooding schedule’s computation tree, indicating that the serial schedule propagates information twice as fast in the code’s underlying graph. Furthermore, asymptotic analysis of the serial schedule’s convergence rate is done using the Density Evolution (DE) algorithm. Applied to various ensembles of LDPC codes, it shows that when working near the ensemble’s threshold, for long enough codes the serial schedule is expected to converge in half the number of iterations compared to the standard flooding schedule. This observation is generally proved for the Binary Erasure Channel (BEC) under some likely assumptions. Finally, an accompanying concentration theorem is proved, justifying the asymptotic DE analysis assumptions. 1
Conventionally, in each low-density parity-check (LDPC) decoding iteration all the variable nodes and subsequently all the check nodes send messages to their neighbors (flooding schedule). An alternative, more efficient, approach is to update the nodes' messages serially (serial schedule). A theoretical analysis of serial message passing decoding schedules is presented. In particular, the evolution of the computation tree under serial scheduling is analyzed. It shows that the tree grows twice as fast in comparison to the flooding schedule's one, indicating that the serial schedule propagates information twice as fast in the code's underlying graph. Furthermore, an asymptotic analysis of the serial schedule's convergence rate is done using the density evolution (DE) algorithm. Applied to various ensembles of LDPC codes, it shows that for long codes the serial schedule is expected to converge in half the number of iterations compared to the standard flooding schedule, when working near the ensemble's threshold. This observation is generally proved for the binary erasure channel (BEC) under some natural assumptions. Finally, an accompanying concentration theorem is proved.
Low-density parity-check (LDPC) codes are usually decoded by running an iterative belief-propagation algorithm over the factor graph of the code. In the traditional message-passing schedule, in each iteration all the variable nodes, and subsequently all the factor nodes, pass new messages to their neighbors. Recently several studies show that serial scheduling, in which messages are generated using the latest available information, significantly improves the convergence speed in terms of number of iterations. It was observed experimentally in several studies that the serial schedule converges in exactly half the number of iterations compared to the standard parallel schedule. In this correspondence we provide a theoretical motivation for this observation by proving it for single-path graphs.
An efficient decoding schedule for low-density parity-check (LDPC) codes that outperforms the conventional approach, in terms of both complexity and performance, is presented. Conventionally, in each iteration, all symbol nodes and, subsequently, all the check nodes, send messages to their neighbors ("flooding schedule"). In contrast, in the proposed method, the updating of nodes is performed according to a serial schedule which propagates the information twice as fast. A density evolution (DE) algorithm for asymptotic analysis of the new schedule is derived, showing that, when working near the code's capacity, the decoder converges in approximately half the number of iterations. In addition, a concentration theorem is proved, showing that, for a randomly chosen serial schedule, code graph, and decoder input, the decoder's performance approaches its expected one as predicted by the DE algorithm, when the code length increases.
Serial schedule based decoding for LDPC codes,in which check nodes are partitioned into groups,converges very fast.However,if there are too many groups,the low degree of parallelism will incur high decoding latency.The extrinsic information transfer(EXIT) chart technique is adopted to find out a balance between convergence rate and decoding latency.EXIT functions for serial schedule based decoding with different group partitions are derived,and a comparison among corresponding EXIT curves is made to estimate the maximum parallelism that serial schedule based decoding may achieve without sacrificing the convergence rate.Simulation results validate the EXIT chart analysis.