Martin Tomlinson, Cen Jung Tjhai, Marcel Ambroze et al. · Greater South Information System · 2017
In this chapter, we discuss the performance of codes under soft and hard decision decoding. Upper and lower bounds on hard and soft decision decoding are discussed. For hard decision decoding, evaluation of the performance of specific codes shows that full decoding produces better performance than the usual bounded distance decoder. An analysis of the upper and lower union bounds on the probability of error for maximum likelihood soft decision decoding shows that contrary to hard decision decoding above relative low values of SNR per information bit, the two bounds coincide. The implications of this observation is that the soft decision decoding performance may be determined for a linear code by the number of minimum Hamming weight codewords without the need to determine the weight distribution of the code. Numerical performance comparisons are made for a wide range of different codes. It is shown that the binomial weight distribution provides a good indicative performance for codes whose weight distribution is difficult to obtain.
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Martin Tomlinson, Cen Jung Tjhai, Marcel Ambroze et al. · Greater South Information System · 2017
In this chapter, we discuss the performance of codes under soft and hard decision decoding. Upper and lower bounds on hard and soft decision decoding are discussed. For hard decision decoding, evaluation of the performance of specific codes shows that full decoding produces better performance than the usual bounded distance decoder. An analysis of the upper and lower union bounds on the probability of error for maximum likelihood soft decision decoding shows that contrary to hard decision decoding above relative low values of SNR per information bit, the two bounds coincide. The implications of this observation is that the soft decision decoding performance may be determined for a linear code by the number of minimum Hamming weight codewords without the need to determine the weight distribution of the code. Numerical performance comparisons are made for a wide range of different codes. It is shown that the binomial weight distribution provides a good indicative performance for codes whose weight distribution is difficult to obtain.
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Caldwell, James · Calhoun: The Naval Postgraduate School Institutional Archive (Naval Postgraduate School) · 2013
Embodiments in accordance with the invention utilize Reed Solomon (RS) forward error correction (FEC) in conjunction with M-ary Bandwidth Efficient Modulation (BEM) schemes and soft decision decoding to improve the robustness of high spectral efficiency communication links. In one embodiment, information symbols in communication data blocks are encoded utilizing Reed Solomon (RS) forward error correction (FEC) coding and transmitted with either M-ary phase shift keying (MPSK) or M-ary quadrature amplitude modulation (MQAM). Using standard Reed Solomon (RS) hard decision decoding, a receiver either correctly decodes the received block or returns a decoding failure. In the event of a decoding failure, soft decision reliability information is used to identify received code symbols with a low probability of being correctly received and to generate new code symbol estimates that are used in the traditional Reed Solomon decoding algorithm.
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Ferdinand Blomqvist · Applicable Algebra in Engineering Communication and Computing · 2021
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Vasyl Semerenko · Eastern-European Journal of Enterprise Technologies · 2018
We propose error correction iteratively decodable cyclic codes (IDCC) that consist of two cyclic Hamming codes with different generator polynomials. As a mathematical apparatus, we apply the theory of linear finite-state machines (LFSM) in binary Galois fields. A generalized decoding algorithm was constructed based on power permutation of bits in the code word and the new technique for combining the codes.By using hard decisions only, it is possible to achieve high speed and simple hardware-software implementation of encoder and decoder on linear feedback shift registers. The IDCC (n, k)-code makes it possible to correct the errors of multiplicity to (n−k). A code word may have arbitrary length: both small and large. Code rate (k/n) is close to one.It was established in the course of research that approaching the theoretical limit (border) by Shannon maximally close significantly increases length of codes, complicates encoders and decoders, increases a delay in decoding, and other problems appear. That is why the main criterion for the optimality of error correction coding is proposed to be those code characteristics that are important for practical application (time and hardware costs, focus on contemporary circuitry and parallel processing). From this point of view, the developed IDCC codes can be considered as an alternative to well-known iterative codes (LDPC codes and turbo codes) whose main advantage is the maximum proximity to the Shannon limit.This is important because at the present stage of development of science and technology one of the relevant scientific and technological problems is the task on ensuring high reliability of data transmission in different systems of digital communication. The proposed codes make it possible to solve the specified task at minimal resource costs and high efficiency.
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Imikolakopoulos X, Xenofon Nikolakopoulos, Tri T. Ha et al. · 1997
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Paddy Farrell, Bahram Honary · Lancaster EPrints (Lancaster University) · 1989
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T. Kaneko, Takeshi Nishijima, Shigeichi Hirasawa · IEEE Transactions on Information Theory · 1997
A new soft-decision maximum-likelihood decoding algorithm is proposed, which generates a set of candidate codewords using hard-decision bounded-distance decoding. By improving the generating method of input vectors for the bounded-distance decoding due to Kaneko et al. (see ibid., vol.40, no.3, p.320-27, 1994), the decoding time complexity is reduced without degradation of the performance. The space complexity is dependent on the bounded-distance decoding.
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Yingnan Qi, Lingjun Kong, Fei Li et al. · Physical Communication · 2025
Cited by 1
Bossert, Martin, Schulz, Rebekka, Bitzer, Sebastian · arXiv (Cornell University) · 2021
The binary primitive BCH codes are cyclic and are constructed by choosing a subset of the cyclotomic cosets. Which subset is chosen determines the dimension, the minimum distance and the weight distribution of the BCH code. We construct possible BCH codes and determine their coderate, true minimum distance and the non-equivalent codes. A particular choice of cyclotomic cosets gives BCH codes which are, extended by one bit, equivalent to Reed-Muller codes, which is a known result from the sixties. We show that BCH codes have possibly better parameters than Reed-Muller codes, which are related in recent publications to polar codes. We study the decoding performance of these different BCH codes using information set decoding based on minimal weight codewords of the dual code. We show that information set decoding is possible even in case of a channel without reliability information since the decoding algorithm inherently calculates reliability information. Different BCH codes of the same rate are compared and different decoding performances and complexity are observed. Some examples of hard decision decoding of BCH codes have the same decoding performance as maximum likelihood decoding. All presented decoding methods can possibly be extended to include reliability information of a Gaussian channel for soft decision decoding. We show simulation results for soft decision list information set decoding and compare the performance to other methods.
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Martin Bossert, Rebekka Schulz, Sebastian Bitzer · IEEE Transactions on Information Theory · 2022
The binary primitive BCH codes are cyclic and are constructed by choosing a subset of the cyclotomic cosets. Which subset is chosen determines the dimension, the minimum distance and the weight distribution of the BCH code. We construct possible BCH codes and determine their coderate, true minimum distance and the non-equivalent codes. A particular choice of cyclotomic cosets gives BCH codes which are, extended by one bit, equivalent to Reed-Muller codes, which is a known result from the sixties. We show that BCH codes have possibly better parameters than Reed-Muller codes, which are related in recent publications to polar codes. We study the decoding performance of these different BCH codes using information set decoding based on minimal weight codewords of the dual code. We show that information set decoding is possible even in case of a channel without reliability information since the decoding algorithm inherently calculates reliability information. Different BCH codes of the same rate are compared and different decoding performances and complexity are observed. Some examples of hard decision decoding of BCH codes have the same decoding performance as maximum likelihood decoding. All presented decoding methods can possibly be extended to include reliability information of a Gaussian channel for soft decision decoding. We show simulation results for soft decision list information set decoding and compare the performance to other methods.
Cited by 18Open access
Ali Al‐Shaikhi, M.A. Kousa · 2004
Product coding produces powerful long codes from short constituent codes. The conventional row-column decoding algorithm of the product code does not exploit its full power of correcting random errors and proposes a modification to the conventional decoding algorithm, which makes it capable of reaching the theoretical error correction capability of the code. In addition to its theoretical significance, the modified algorithm is shown to provide a gain of 0.5 dB over the conventional algorithm for AWGN channels.
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Demiray, Can · OpenMETU (Middle East Technical University) · 2019
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Alexander Barg, Evgenii Krouk, Henk C. A. van Tilborg · 2002
We study a general method of minimum distance decoding of linear codes that instead of decoding the original code recovers the transmitted codeword by a number of decodings of shortened codes. We present an implementation of this method whose complexity for long linear codes has the smallest known value for any code rate R, 0<R<1.
Cited by 3
Sheikh, Alireza, Amat, Alexandre Graell i, Liva, Gianluigi · arXiv (Cornell University) · 2017
We consider probabilistic amplitude shaping (PAS) as a means of increasing the spectral efficiency of fiber-optic communication systems. In contrast to previous works in the literature, we consider probabilistic shaping with hard decision decoding (HDD). In particular, we apply the PAS recently introduced by Böcherer \emph{et al.} to a coded modulation (CM) scheme with bit-wise HDD that uses a staircase code as the forward error correction code. We show that the CM scheme with PAS and staircase codes yields significant gains in spectral efficiency with respect to the baseline scheme using a staircase code and a standard constellation with uniformly distributed signal points. Using a single staircase code, the proposed scheme achieves performance within $0.57$--$1.44$ dB of the corresponding achievable information rate for a wide range of spectral efficiencies.
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Tomer Raviv, Nir Raviv, Y. Be'ery · arXiv (Cornell University) · 2020
Ensemble models are widely used to solve complex tasks by their decomposition into multiple simpler tasks, each one solved locally by a single member of the ensemble. Decoding of error-correction codes is a hard problem due to the curse of dimensionality, leading one to consider ensembles-of-decoders as a possible solution. Nonetheless, one must take complexity into account, especially in decoding. We suggest a low-complexity scheme where a single member participates in the decoding of each word. First, the distribution of feasible words is partitioned into non-overlapping regions. Thereafter, specialized experts are formed by independently training each member on a single region. A classical hard-decision decoder (HDD) is employed to map every word to a single expert in an injective manner. FER gains of up to 0.4dB at the waterfall region, and of 1.25dB at the error floor region are achieved for two BCH(63,36) and (63,45) codes with cycle-reduced parity-check matrices, compared to the previous best result of [1].
Cited by 1Open access
J J W Lagendijk, Yunus Can Gültekin, Alexios Balatsoukas‐Stimming et al. · 2025
Stall patterns are known to cause an error floor in hard decision decoding of the OFEC code. We propose a novel stall pattern removal algorithm that lowers the error floor of state-of-the-art algorithms by an order of magnitude. ©2025 The Author(s)
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Alireza Sheikh, Alexandre Graell i Amat, Gianluigi Liva et al. · Journal of Lightwave Technology · 2017
We consider probabilistic amplitude shaping (PAS) as a means of increasing the spectral efficiency of fiber-optic communication systems. In contrast to previous works in the literature, we consider probabilistic shaping with hard decision decoding (HDD). In particular, we apply the PAS recently introduced by Böcherer et al. to a coded modulation (CM) scheme with bit-wise HDD that uses a staircase code as the forward error correction code. We show that the CM scheme with PAS and staircase codes yields significant gains in spectral efficiency with respect to the baseline scheme using a staircase code and a standard constellation with uniformly distributed signal points. Using a single staircase code, the proposed scheme achieves performance within 0.57-1.44 dB of the corresponding achievable information rate for a wide range of spectral efficiencies.
Cited by 33Open access
Rinu Jose, Ameenudeen Pe · 2015
This article compares the Bit Error Rate (BER) performance of soft and hard decision decoding algorithms of LDPC codes on AWGN channel at different code rates and Signal to Noise Ratio (SNR) levels. Even though, hard decision decoding algorithm is computationally simple, its BER performance is not appreciable. Devising soft decision decoding algorithms which are simple and good in BER performance requires comparison of probabilistic and log domain methods. Towards this, a code word is generated through modulo(2) addition between message bits and generator matrix. After Binary Phase Shift Keying (BPSK) modulation the AWGN noise is introduced to the modulated code word. BER performance is computed by comparing the message decoded by soft and hard decision algorithms with the transmitted message. The experiment is conducted in MATLAB. Soft decision decoding algorithm in log domain provides better BER performance than hard decision decoding algorithm regardless of the SNR level.
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M.A. El-Agamy, E. Munday · Electronics Letters · 1984
A probabilistic hard-decision decoding algorithm based on the weight distribution of binary block codes and the random error distribution in the channel is briefly described. It reduces the number of look-up iterations performed in the conventional exhaustive search table look-up minimum distance decoder.
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