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IEEE Transactions on Communications

Reliability-Based Schedule for Bit-Flipping Decoding of Low-Density Parity-Check Codes

A. Nouh, Amir H. Banihashemi

Published Dec 1, 2004• 24 citations
Publisher

Abstract

A reliability-based message-passing schedule for iterative decoding of low-density parity-check codes is proposed. Simulation results for bit-flipping algorithms (with binary messages) show that a reliability-based schedule can provide considerable improvement in performance and decoding speed over the so-called flooding (parallel) schedule, as well as the existing graph-based schedules. The cost associated with this improvement is negligible and is equivalent to having a two-bit representation for initial messages, instead of the standard one bit for hard-decision algorithms, only at the first iteration (all the exchanged messages are still binary).

DOI
10.1109/tcomm.2004.838704

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IEEE Transactions on Information Theory•Nov 1, 2007•155 citations
A reliability-based message-passing schedule for iterative decoding of low-density parity-check codes is proposed. Simulation results for bit-flipping algorithms (with binary messages) show that a reliability-based schedule can provide considerable improvement in performance and decoding speed over the so-called flooding (parallel) schedule, as well as the existing graph-based schedules. The cost associated with this improvement is negligible and is equivalent to having a two-bit representation for initial messages, instead of the standard one bit for hard-decision algorithms, only at the first iteration (all the exchanged messages are still binary).
A reliability-based message-passing schedule for iterative decoding of low-density parity-check codes is proposed. Simulation results for bit-flipping algorithms (with binary messages) show that reliability-based schedule can provide considerable improvement in performance and decoding speed over the so-called flooding (parallel) schedule as well as the existing graph-based schedules. The cost associated with this improvement is negligible and is equivalent to having a 2-bit representation for initial messages, instead of the standard 1-bit for hard-decision algorithms, only at the first iteration (all the exchanged messages are still binary).
The best known practical algorithm for the decoding of low-density parity-check (LDPC) codes is the iterative sum-product or belief propagation algorithm, operating on a Tanner graph (TG) of the code. Conventionally, in each iteration, all the symbol nodes and subsequently all the check nodes in the TG pass new messages to their neighbors (the so-called "flooding schedule"). We propose a new message-passing schedule, called "probabilistic schedule." Unlike flooding, the probabilistic schedule operates based on the structure of the TG, and probabilistically balances the frequency at which different symbol nodes update their outgoing messages in accordance with their girths. Our results show that, particularly for short block lengths, the new schedule offers a much better performance/complexity trade-off. For a particular example of a (1268,456) code, at no cost in complexity, the probabilistic schedule not only decreases both the bit and message error rates by an order of magnitude, but also reduces the number of undetected errors considerably. This work shows the importance of scheduling in the performance of iterative decoding algorithms and suggests that a schedule which matches the structure of the TG can substantially improve the performance/complexity trade-off in the decoding of short LDPC codes.
The best known practical algorithm for the decoding of low-density parity-check (LDPC) codes is the iterative sum-product or belief propagation algorithm, operating on a Tanner graph (TG) of the code. Conventionally, in each iteration, all the symbol nodes and subsequently all the check nodes in the TG pass new messages to their neighbors (the so-called "flooding schedule"). We propose a new message-passing schedule, called "probabilistic schedule". Unlike flooding, the probabilistic schedule operation is based on the structure of the TG, and probabilistically balances the frequency at which different symbol nodes update their outgoing messages in accordance with their girths. Our results show that, particularly for short block lengths, the new schedule offers a much better performance/complexity trade-off. For a particular example of a (1268, 456) code, at no cost in complexity, the probabilistic schedule not only decreases both the bit and message error rates by an order of magnitude, but also reduces the number of undetected errors considerably. This work shows the importance of scheduling in the performance of iterative decoding algorithms and suggests that a schedule which matches the structure of the TG can substantially improve the performance/complexity trade-off in the decoding of short LDPC codes.
This letter proposes a novel two-bit weighted bit-flipping algorithm (TB-WBFA) for low-density parity-check (LDPC) codes on the binary symmetric channel. The proposed TB-WBFA produces reliability bits for the bit-decision results and syndrome values at bit and check nodes, respectively. The reliability bits are exchanged between bit and check nodes as the decoding proceeds. The message update in check nodes is carefully devised with simple bitwise operations, which are especially suitable for high-speed operations. It will be demonstrated that the proposed TB-WBFA achieves a significant performance improvement over existing bit-flipping decoding algorithms by conducting performance comparisons for LDPC codes under various setups, i.e., different rates, lengths, and structures.
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.