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Computer Era

Local Loop Removal from Irregular LDPC Codes

Chunjiang Duanmu

Published Jan 1, 2011• 0 citations
OpenAlex

Abstract

In low-density parity-check(LDPC) codes,the small loops between low degree nodes are more detrimental to the decoding performance than those between high degree nodes.In order to reduce small loops,we propose a method of exchanging the edges between nodes.It first removes the small loops between low degree nodes as much as possible,and then removes the small loops from whole LDPC codes under the condition of ensuring the smallest loop between low degree nodes not to be changed.Finally,the simulation result of constructing LDPC codes by the method is compared with that by only removing the small loops from whole LDPC codes.

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Abstract: Small stopping sets have been proved to be harmful to the error floor performance of a finite-length irregular low-density parity-check (LDPC) code over the binary erasure channel (BEC). On the additive white gaussian noise (AWGN) channel, small stopping sets are expected to have a similar effect. This paper proposes an algorithm that iteratively removes the small-stopping-set-inducing patterns from the graph of a randomly generated irregular LDPC code by means of node exchange, aiming at enlarging the average size of stopping sets in this code. Computer simulation results show that the short-length LDPC codes after our processing achieve a considerable performance improvement in the low-BER region compared to the randomly generated codes. Key words: Error floor, irregular LDPC codes, iterative processing, small stopping set 1

•Jan 1, 2005•1 citation
In low-density parity-check(LDPC) codes,the small loops between low degree nodes are more detrimental to the decoding performance than those between high degree nodes.In order to reduce small loops,we propose a method of exchanging the edges between nodes.It first removes the small loops between low degree nodes as much as possible,and then removes the small loops from whole LDPC codes under the condition of ensuring the smallest loop between low degree nodes not to be changed.Finally,the simulation result of constructing LDPC codes by the method is compared with that by only removing the small loops from whole LDPC codes.
Recently, the concept of layered decoding schedule for Low-Density Parity-Check codes has been introduced. But the advantage of layered decoding schedule for irregular LDPC codes is not as obvious as regular LDPC codes. The major drawback of the layered irregular LDPC codes versus the layered regular LDPC codes is its comparative low convergence decoding speed. Simulation results show that different bit node degrees of irregular LDPC codes significantly contribute to the decoding performance. The decoding performance of bit nodes with different degrees is of great difference. Bit nodes with small degrees always converge slower than larger ones. In this paper, we propose an optimized decoding schedule for irregular LDPC codes to accelerate the decoding convergence rate. Meanwhile, for the irregular LDPC decoder, the faster decoding speed means a higher throughput and almost the same error performance.
It is hypothesised that small loops in the graphical representations of low-density parity-check codes are detrimental to the code's performance. We demonstrate a procedure for removing such loops from the codes. An algorithm based on the code's adjacency matrix is used to locate unwanted loops, and then certain edges within the graph are exchanged to eliminate those loops (without simultaneously creating any others). This process can be repeated until there are no loops remaining with a size less than a particular limit. A comparison of some theoretical and experimental values for this limit is given.
Over the past two decades, irregular low-density parity-check (LDPC) codes have been hardly able to decode information corrupted by insertion and deletion (ID) errors without markers. Surprisingly, in this paper, we bring to light the existence of irregular LDPC codes that approach the theoretical limit of the channel with ID errors even without markers. These codes contain high fractions of low-degree check nodes that do not appear in irregular codes for other channels. This motivates us to investigate the contribution of low-degree check nodes to correcting ID errors. The investigation provides the following interesting result: degree-2 check nodes are critical to approaching the theoretical limit even without markers, codes with only degree-3, 4, or more check nodes provide moderate decoding performance, and codes with only degree-5 or more check nodes can hardly correct ID errors. Finally, we present simulation results that confirm the excellent decoding performance of the irregular codes without markers.
Trapping sets strongly degrade performance of low-density parity check (LDPC) codes in the low-error-rate region. This creates significant difficulties for the deployment of LDPC codes to low-error-rate applications such as storage and wireless systems with no or limited retransmission options. We propose a novel technique for breaking trapping sets based on collaborative decoding that utilizes two different decoding modes. While the main decoding mode executes message passing based on the original parity check matrix of the corresponding LDPC code, the sub-decoding mode operates on a modified parity check matrix formed by removing a portion of check nodes in the factor graph representation of the given code. The modified parity check matrix is designed to promote a passing of correct information into erroneous variable nodes in the trapping set. Theoretical properties of the proposed trapping-set-breaking technique have been established based on the notion of the improved separation for the trapped variable nodes. Simulation results show that the proposed collaborative LDPC decoding scheme switching between the two decoding modes back and forth effectively breaks dominant trapping sets of various known types of regular and irregular LDPC codes.
Abstract: Small stopping sets have been proved to be harmful to the error floor performance of a finite-length irregular low-density parity-check (LDPC) code over the binary erasure channel (BEC). On the additive white gaussian noise (AWGN) channel, small stopping sets are expected to have a similar effect. This paper proposes an algorithm that iteratively removes the small-stopping-set-inducing patterns from the graph of a randomly generated irregular LDPC code by means of node exchange, aiming at enlarging the average size of stopping sets in this code. Computer simulation results show that the short-length LDPC codes after our processing achieve a considerable performance improvement in the low-BER region compared to the randomly generated codes. Key words: Error floor, irregular LDPC codes, iterative processing, small stopping set 1