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International Conference on Communications

Reliability-based schedule for decoding low-density parity-check codes

A. Nouh, Amir H. Banihashemi

Published Jan 1, 2004• 0 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 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).

DOI
10.1109/icc.2004.1312528

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IEEE Communications Letters•Jun 1, 2013•23 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 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).
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).
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.
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.
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.
Abstract — Low-Density Parity-Check (LDPC) codes are usually decoded by running an iterative belief-propagation, or message-passing, algorithm over the factor graph of the code. The traditional message-passing schedule consists of updating all the variable nodes in the graph, using the same pre-update information, followed by updating all the check nodes of the graph, again, using the same pre-update information. Recently several studies show that sequential scheduling, in which messages are generated using the latest available information, significantly improves the convergence speed in terms of number of iterations. Sequential scheduling raises the problem of finding the best sequence of message updates. This paper presents practical scheduling strategies that use the value of the messages in the graph to find the next message to be updated. Simulation results show that these informed update sequences require significantly fewer iterations than standard sequential schedules. Complexity and implementability issues are also addressed. Index Terms — Belief propagation-algorithm, messagepassing schedule, error-control codes, low-density paritycheck codes. I.