Weight distribution and performance of the iterated product of single-parity-check codes

Caire, Giuseppe; Taricco, G.; Battail, Gérard

doi:10.1109/ctmc.1994.512606

Cited by 25 publications
(22 citation statements)

~~References 7 publications~~

~~Supporting~~

~~Mentioning~~

~~Contrasting~~

~~Order By: Relevance~~

“…The observation that a TPC/SPC code can be effectively viewed as a type of structured LDPC code [4], [14] where each row in each dimension satisfies a check, leads to a convenient adoption of the message-passing algorithm (or the sum-product algorithm) from LDPC codes. Since each bit is expressed as the modulo-sum of the rest of the bits in the check, this messagepassing decoding algorithm is, in fact, an extension of replication decoding [15]. The exact decoding algorithm can be found in Appendix I.…”

Section: A Spc-based Product Code Structure and Propertiesmentioning
confidence: 99%

“…The simple and regular structure of a TPC/SPC code makes it possible to analyze the code properties. In particular, the weight spectrum of a 2-D TPC/SPC code with parameter can be calculated by the following equation [15]:…”

Section: A Spc-based Product Code Structure and Propertiesmentioning
confidence: 99%

“…It has been shown that the weight distribution of TPC/SPC codes asymptotically approaches that of a random code if the dimension of the code and the lengths of all component codes go to infinity [15]. However, increasing the dimension decreases the code rate and is therefore not of interest in the design of high-rate codes.…”

Section: A Spc-based Product Code Structure and Propertiesmentioning
confidence: 99%

“…Let , denote the input output weight enumerator (IOWE) of the th SPC branch code (parallelly concatenated in the outer code). The IOWE of the outer codewords, , averaged over the code ensemble is given as (15) where is the input sequence length. Define the input output weight transfer probability (IOWTP) of the th branch code, , as the probability that a particular input sequence of weight is mapped to an output sequence of weight (16) Substituting (16) in (15), we get (17) For each branch where SPC codewords are combined, the IOWE function is given as (assuming even parity check) (18) (19) where the coefficient of the term denotes the number of codewords with input weight and output weight .…”

Section: B Performance Under ML Decodingmentioning
confidence: 99%

See 3 more Smart Citations
Product Accumulate Codes: A Class of Codes With Near-Capacity Performance and Low Decoding Complexity
Li
¹
,
Narayanan
²
,
Georghiades
³

2004
IEEE Trans. Inform. Theory
86
2
81
0
View full text Add to dashboard Cite
Abstract-We propose a novel class of provably good codes which are a serial concatenation of a single-parity-check (SPC)-based product code, an interleaver, and a rate-1 recursive convolutional code. The proposed codes, termed product accumulate (PA) codes, are linear time encodable and linear time decodable. We show that the product code by itself does not have a positive threshold, but a PA code can provide arbitrarily low bit-error rate (BER) under both maximum-likelihood (ML) decoding and iterative decoding. Two message-passing decoding algorithms are proposed and it is shown that a particular update schedule for these message-passing algorithms is equivalent to conventional turbo decoding of the serial concatenated code, but with significantly lower complexity. Tight upper bounds on the ML performance using Divsalar's simple bound and thresholds under density evolution (DE) show that these codes are capable of performance within a few tenths of a decibel away from the Shannon limit. Simulation results confirm these claims and show that these codes provide performance similar to turbo codes but with significantly less decoding complexity and with a lower error floor. Hence, we propose PA codes as a class of prospective codes with good performance, low decoding complexity, regular structure, and flexible rate adaptivity for all rates above 1 2.
show abstract

Section: A Spc-based Product Code Structure and Propertiesmentioning
confidence: 99%

Section: B Performance Under ML Decodingmentioning
confidence: 99%

See 2 more Smart Citations
Product Accumulate Codes: A Class of Codes With Near-Capacity Performance and Low Decoding Complexity
Li
¹
,
Narayanan
²
,
Georghiades
³

2004
IEEE Trans. Inform. Theory
86
2
81
0
View full text Add to dashboard Cite
Abstract-We propose a novel class of provably good codes which are a serial concatenation of a single-parity-check (SPC)-based product code, an interleaver, and a rate-1 recursive convolutional code. The proposed codes, termed product accumulate (PA) codes, are linear time encodable and linear time decodable. We show that the product code by itself does not have a positive threshold, but a PA code can provide arbitrarily low bit-error rate (BER) under both maximum-likelihood (ML) decoding and iterative decoding. Two message-passing decoding algorithms are proposed and it is shown that a particular update schedule for these message-passing algorithms is equivalent to conventional turbo decoding of the serial concatenated code, but with significantly lower complexity. Tight upper bounds on the ML performance using Divsalar's simple bound and thresholds under density evolution (DE) show that these codes are capable of performance within a few tenths of a decibel away from the Shannon limit. Simulation results confirm these claims and show that these codes provide performance similar to turbo codes but with significantly less decoding complexity and with a lower error floor. Hence, we propose PA codes as a class of prospective codes with good performance, low decoding complexity, regular structure, and flexible rate adaptivity for all rates above 1 2.
show abstract

“…Weight distribution and performance of the iterated product of single-parity-check codes Abstract of [92] We consider the iterated product of binary singleparity-check (SPC) codes. We show that their weight distribution asymptotically approaches that of random coding if the smallest code length in the product approaches infinity.…”

Section: Abstract Of [90]mentioning
confidence: 99%

Bibliographie / Bibliography
2015
VRÜ
0
0
0
0
View full text Add to dashboard Cite

IntroductionFrançais. J'ai dressé une liste de mes publications pour essayer de m'y retrouver. Elle peut avoir aussi une certaine utilité pour d'autres. Cette liste està peu près complète, sauf pour les publications les plus anciennes. Je n'y ai pas inclus des rapports internes que j'ai rédigésà la Thomson (entre 1966Thomson (entre et 1973 sur des problèmes plus divers que ceux de la liste, mais seulement mentionné les titres de quelques brevets de cette période. La langue employée dans le titre est toujours celle de l'article. Des sommaires de certaines publications (estimées les plus importantes, surtout parmi les plus récentes) précèdent la liste proprement dite. Pour la plupart des articlesécrits en français, le résumé en anglais publié avec l'article ('abstract' ou 'summary') est joint au sommaire français ; si la langue de la publication est l'anglais, il n'y a le plus souvent qu'un sommaire anglais. J'ai aussi mentionné quelques travaux non terminés qui ont bien peu de chance de l'être un jour, ainsi que des projets dont l'avenir est incertain.English. I compiled a list of publications in order to find my own way in my previous work. It may also have some usefulness for other people. This list is almost complete, except for the oldest publications. I did not include in it reports I wrote when working at Thomson (between 1966 and 1973) concerning more diverse problems than those of the list, but I mentioned the titles of some patents of this time. The language of the title is always that of the paper. Summaries or abstracts of certain publications (those deemed the most important, especially among the most recent ones) precede the list itself. For most of the papers written in French, the abstract or summary in English is appended to the French summary as it was when the paper was published; if the publication language is English, only an English summary is generally provided. I also mentioned few unfinished works which have little chance to be once completed, as well as projects of uncertain future.Sur l'emploi des signauxà bande limitée dans la théorie des communications Sommaire de [7] On rappelle d'abord les difficultés et les paradoxes rencontrés dans l'utilisation des signaux a bande limitée en théorie des communications. L'examen critique du concept de spectre suggère de les interpréter en tenant compte du retard, en principe infini, impliqué dans leur définition même. L'hypothèse d'un retard infini paraît suffire en effetà les résoudre. On montre ensuite qu'on préfère systématiquement, dans la technique des communications, la limitation du spectreà la limitation (antagoniste) du retard, au profit de la qualité de transmission (notamment dans les systèmes multiplex).Les signaux réels pouvant alorsêtre considérés comme des approximationsà retard fini des signauxà bande limitée, les seconds définissent une représentation pour les premiers, approchée asymptotiquement quand le retard accepté pour les signaux réels tend vers l'infini. On montre sa simplicité et sa généralité, ainsi que l'intérêt de...

~~show abstract~~

Recoverability study of SPC product codes under erasure decoding
Amutha
¹
,
Verraraghavan
²
,
Srivatsa³
2005
Information Sciences
5
0
6
0
View full text Add to dashboard Cite

Weight distribution and performance of the iterated product of single-parity-check codes

Cited by 25 publications

References 7 publications

Product Accumulate Codes: A Class of Codes With Near-Capacity Performance and Low Decoding Complexity

Product Accumulate Codes: A Class of Codes With Near-Capacity Performance and Low Decoding Complexity

Bibliographie / Bibliography

Recoverability study of SPC product codes under erasure decoding

Contact Info

Product

Resources

About