Optimized Message Passing Schedules for LDPC Decoding

Abstract

Abstract-The major drawback of the LDPC codes versus the turbo-codes is their comparative low convergence speed: 25-30 iterations vs. 8-10 iterations for turbo-codes. Recently, Hocevar showed by simulations that the convergence rate of the LDPC decoder can be accelerated by exploiting a 'turbo-scheduling' applied on the bit-node messages (rows of the parity check matrix). In this paper, we show analytically that the convergence rate for this type of scheduling is about two times increased for most of the regular LDPC codes. Second we prove that 'turbo-scheduling' applied on the rows of the parity check matrix is identical belief propagation algorithm as standard message passing algorithm. Furthermore, we propose two new message passing schedules: 1) a turbo-scheduling is applied on the checknode messages (columns of the parity check matrix); 2) a hybrid version of both previous schedules where the turbo-effect is applied on both check-nodes and bit-nodes. Frame error rate simulations validate the effectiveness of the proposed schedules.

Distributed Decoding in Cooperative Communications

“…The layered belief propagation algorithm is a variation of the standard belief propagation [8], and achieves about two times faster decoding convergence due to the optimized scheduling of reliability messages [9]. The PCM can be viewed as a group of concatenated horizontal layers in which every layer represents the component code.…”

Configurable, High Throughput, Irregular LDPC Decoder Architecture: Tradeoff Analysis and Implementation

“…This algorithm is a variation of the standard belief propagation [4], and achieves about two times faster decoding convergence due to the optimized scheduling of reliability messages [11]. The PCM can be viewed as a group of concatenated horizontal layers as shown in Fig.…”

LDPC Decoders with Informed Dynamic Scheduling

“…Sequential scheduling was introduced as a sequence of checknode updates in [3] and [4] and as a sequence of variable-node updates in [5] and [6]. It is also presented in [7] under the name of Layered BP (LBP), in [8] and [9] as serial schedule, in [10] as row message passing, column message passing and row-column message passing, among others.…”

“…Monte-Carlo simulations and theoretical analysis in [3]- [10] show that sequential scheduling converges twice as fast as flooding when used in LDPC decoding. It has also been shown that sequential updating doesn't increase the decoding complexity per iteration, thus allowing the convergence speed increase at no cost [10], [11].…”

“…It has also been shown that sequential updating doesn't increase the decoding complexity per iteration, thus allowing the convergence speed increase at no cost [10], [11]. Although the literature listed above presents a variety of sequential schedules, they have very similar performance results [10].…”