Search and Determination of Convolutional Self-Doubly Orthogonal Codes for Iterative Threshold Decoding

A class of orthogonal convolutional codes using a multi shift-register encoder and featuring self-doubly-orthogonal properties is analyzed under iterative decoding. The lower bounds of error performances of these codes can be approached within typically three to five iterations at moderate signal-tonoise ratios using either iterative threshold (TH) decoding or belief propagation (BP) decoding. Compared with iterative BP decoding, it is shown that iterative threshold decoding for these codes yields a much lower complexity at the same decoding latency.

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“…Table I lists four M-CSDO codes of coding rate 1/2 which have been determined using heuristic search algorithms [2], [7]. Table I …”

Section: Code Definitionmentioning

confidence: 99%

Error performances of multi shift-register convolutional self-doubly-orthogonal codes

Haccoun

Cardinal

2009

IEEE Commun. Lett.

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“…As the error-correcting capability of the new codes depends essentially on the dimension J of the vector generator of the R = 1 2 code [8], and because the code constraint length (or "span" of the code) has a direct impact on the latency of the system, it is of great importance to search for rate R = 1 2 systematic Convolutional Self-Doubly Orthogonal (CDO) codes (and their variants) having the shortest possible spans for any given J number of connections. Since no systematic deterministic method for solving this problem is currently known, the code searching is usually conducted using heuristic search algorithms [8], [9].…”

Section: Introductionmentioning

confidence: 99%

“…Since no systematic deterministic method for solving this problem is currently known, the code searching is usually conducted using heuristic search algorithms [8], [9]. However, although finding a CDO code is relatively easy, determining the shortest span codes for a given J has eluded analysis and is still an open problem.…”

Section: Introductionmentioning

confidence: 99%

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Efficient Parallel Search Algorithm for Determining Optimal R=1/2 Systematic Convolutional Self-Doubly Orthogonal Codes

Kowarzyk

Belanger

Haccoun

et al. 2013

IEEE Trans. Commun.

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A novel parallel and implicitly-exhaustive search algorithm for finding, in systematic form, rate R = 1 2 optimalspan Convolutional Self-Doubly Orthogonal (CDO) codes and Simplified Convolutional Self-Doubly Orthogonal (S-CDO) codes is presented. In order to obtain high-performance low-latency codecs with these codes, it is important to minimize their constraint length (or "span") for a given J number of generator connections. The proposed exhaustive algorithm uses algorithmic enhancements over the best previously published searching techniques, yielding new and improved codes: we were able to obtain new optimal-span CDO/S-CDO codes (having order J ∈ {9} and J ∈ {10, 11} respectively), as well as new codes having the shortest spans published to date for higher values of J (J ∈ {10, 12, ..., 17} and J ∈ {12, ..., 20} for CDO and S-CDO codes respectively). The new codes and their error performance are provided. An analysis of the evolution of the CDO/S-CDO code error performance as J increases is presented, and the shortest CDO/S-CDO code span values for each given J are compared.

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“…Iterative decoding of CSOCs using either threshold decoding or belief propagation (BP) allows an improvement of the error performance [4], [5]. For lowcomplexity iterative threshold decoding without interleaving, convolutional self-doubly-orthogonal codes (CSO2Cs) were proposed as an extension of CSOCs [6], [7]. It has been shown that the double orthogonality property of CSO2Cs improves the code structure by maximizing the number of independent observations between successive decoding iterations.…”

Section: Introductionmentioning

confidence: 99%

Procedures for Efficient Iterative Decoding of Orthogonal Convolutional Codes

Haccoun

Cardinal

2006

2006 IEEE International Conference on Communications

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A procedure for the forward-only iterative belief propagation decoding of orthogonal convolutional codes is presented. It can be dramatically simplified to perform the iterative threshold decoding of convolutional self-doubly-orthogonal codes without interleaving. These procedures can help implement iterative decoders efficiently using a serial concatenation of onestep BP decoders or one-step threshold decoders, respectively. Simulations have shown that the error performance of orthogonal convolutional codes can be improved by iterative decoding whether based on belief propagation decoding or threshold decoding. For convolutional self-doubly-orthogonal codes, iterative threshold decoding can achieve the same error performance as iterative belief propagation decoding, but with greatly reduced decoding complexity, allowing an advantageous tradeoff between implementation complexity and latency.

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Search and Determination of Convolutional Self-Doubly Orthogonal Codes for Iterative Threshold Decoding

Cited by 17 publications

References 4 publications

Error performances of multi shift-register convolutional self-doubly-orthogonal codes

Error performances of multi shift-register convolutional self-doubly-orthogonal codes

Efficient Parallel Search Algorithm for Determining Optimal R=1/2 Systematic Convolutional Self-Doubly Orthogonal Codes

Procedures for Efficient Iterative Decoding of Orthogonal Convolutional Codes

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