Segmentation-Discarding Ordered-Statistic Decoding for Linear Block Codes

Yue, Chentao; Shirvanimoghaddam, Mahyar; Li, Yonghui; Vucetic, Branka

doi:10.1109/globecom38437.2019.9014173

Cited by 23 publications

(4 citation statements)

References 19 publications

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“…This list is notably determined thanks to the computation of joint error probabilities for the most reliable bits, and allows to process only the most probable candidate codewords. In [16], the most reliable bits are partitioned into segments according to reliability thresholds depending of the received noisy codeword. Only some of the segments are then selected for flipping.…”

Section: Complexity Reductionmentioning

confidence: 99%

Sets of complementary LLRs to improve OSD post-processing of BP decoding

Rosseel,

Mannoni,

Savin

et al. 2023

2023 12th International Symposium on Topics in Coding (ISTC)

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This article deals with Ordered Statistics Decoding (OSD) applied to the soft outputs of the Belief Propagation (BP) algorithm. We first model the weighted sum of the a posteriori LLRs across BP decoding iterations into a neuron. The neuron is then trained with the focal loss to compute for each BP decoding failure a set of accumulated Log Likelihood Ratios (LLRs) suited for OSD post-processing. Then, we propose a recursive selection procedure of LLRs sets, for multiple OSD post-processing. This selection is carried out from the sets of a posteriori LLRs calculated at each BP iteration, and from the accumulated LLRs optimized for the OSD, based on their joint probabilities of failure with OSD post-processing. An OSD is then applied to each set of LLRs belonging to the selection. In addition, we propose to reduce the OSD post-processing decoding complexity without significantly degrading its performance. Our results show that this new decoding method provides an effective way to bridge the gap to maximum likelihood decoding for short and long Low Density Parity Check (LDPC) codes.

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Section: Complexity Reductionmentioning

confidence: 99%

Sets of complementary LLRs to improve OSD post-processing of BP decoding

Rosseel,

Mannoni,

Savin

et al. 2023

2023 12th International Symposium on Topics in Coding (ISTC)

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show abstract

“…These are mainly to terminate the decoding early, when a suitable candidate codeword is found, and to discard TEPs, which are less likely to generate promising codeword candidates. Other approaches introduced in [58], [59] can also be used to further reduce the complexity by searching through the TEPs in an optimal manner, which will result in finding the best codeword estimate faster. An efficient implementation in C has shown that the OSD decoding with sufficient and necessary conditions can run an order-5 OSD in a few µs per codeword [60].…”

Section: Osd Decoding Of Pr Codesmentioning

confidence: 99%

Primitive Rateless Codes

Shirvanimoghaddam

2021

IEEE Trans. Commun.

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In this paper, we propose primitive rateless (PR) codes. A PR code is characterized by the message length and a primitive polynomial over GF(2), which can generate a potentially limitless number of coded symbols. We show that codewords of a PR code truncated at any arbitrary length can be represented as subsequences of a maximum-length sequence (m-sequence). We characterize the Hamming weight distribution of PR codes and their duals and show that for a properly chosen primitive polynomial, the Hamming weight distribution of the PR code can be well approximated by the truncated binomial distribution. We further find a lower bound on the minimum Hamming weight of PR codes and show that there always exists a PR code that can meet this bound for any desired codeword length. We provide a list of primitive polynomials for message lengths up to 40 and show that the respective PR codes closely meet the Gilbert-Varshamov bound at various rates. Simulation results show that PR codes can achieve similar block error rates as their BCH counterparts at various signal-to-noise ratios (SNRs) and code rates. PR codes are rate-compatible and can generate as many coded symbols as required; thus, demonstrating a truly rateless performance.

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“…Recently, a threshold-based OSD decoder was able to reduce the number of tested codewords [10]. CA-OSD [10] and segmentation-discarding decoding [11] limit the number of valid codewords to improve performance. Probability-based OSD [12] calculates the promising probability and success probability to discard the candidate codewords.…”

Section: Introductionmentioning

confidence: 99%

Pre-Configured Error Pattern Ordered Statistics Decoding for CRC-Polar Codes

Li,

Niu,

Han

et al. 2023

Entropy

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In this paper, we propose a pre-configured error pattern ordered statistics decoding (PEPOSD) algorithm and discuss its application to short cyclic redundancy check (CRC)-polar codes. Unlike the traditional OSD that changes the most reliable independent symbols, we regard the decoding process as testing the error patterns, like guessing random additive noise decoding (GRAND). Also, the pre-configurator referred from ordered reliability bits (ORB) GRAND can better control the range and testing order of EPs. An offline–online structure can accelerate the decoding process. Additionally, we also introduce two orders to optimize the search order for testing EPs. Compared with CRC-aided OSD and list decoding, PEPOSD can achieve a better trade-off between accuracy and complexity.

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Segmentation-Discarding Ordered-Statistic Decoding for Linear Block Codes

Cited by 23 publications

References 19 publications

Sets of complementary LLRs to improve OSD post-processing of BP decoding

Sets of complementary LLRs to improve OSD post-processing of BP decoding

Primitive Rateless Codes

Pre-Configured Error Pattern Ordered Statistics Decoding for CRC-Polar Codes

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