Convolutional Self-doubly Orthogonal Codes Research Articles

R=1/2 Self-Doubly 조직 직교 길쌈부호를 찾는 효율적인 최적 스팬 알고리듬

In this paper, a new method for finding optimal and short span in Convolutional Self-Doubly Orthogonal(CDO) codes are proposed. This new algorithm based on Parallel Implicitly-Exhaustive search, where we applied dynamic search space reduction methods in order to reduce computational time for finding Optimal Span for R=1/2 rate CDO codes. The simulation results shows that speedup and error correction performance of the new algorithm is better.

Optimizing the Parallel Tree-Search for Finding Shortest-Span Error-Correcting CDO Codes

Finding optimal/short-span Convolutional Self-Doubly Orthogonal (CDO) codes and Simplified-CDO (S-CDO) codes for a specified order J is computationally very challenging. This paper describes several optimizations that were applied to an implicitly-exhaustive search algorithm in order to reduce the time required for finding these types of codes. The resulting high-performance parallel implementation provides an impressive speedup that is greater than 16 300 (CDO, ${\rm J} = 7$ ) and 6300 (S-CDO, ${\rm J} = 8$ ) over the reference implicitly-exhaustive search algorithm, and greater than 2000 $({\rm J} = 17)$ over the fastest published CDO validation function used in high-performance pseudorandom search algorithms. These speedups are achieved through enhancements in the deterministic search-space reduction, and a vastly improved validation function that makes use of a novel data structure for enabling data-reuse and incremental computations. The resulting validation function speedup is greater than 60 000 (S-CDO, ${\rm J} = 17$ ) and 190 000 (CDO, ${\rm J} = 17$ ) when compared to its reference implementation. The combination of optimizations and load-balancing techniques allowed us to leverage hundreds of processor cores in order to complete an exhaustive search over a search space that is some $10^{14}$ times larger than what was previously possible.

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

A novel parallel and implicitly-exhaustive search algorithm for finding, in systematic form, rate R=1/2 optimal-span 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.

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

A novel parallel and implicitly-exhaustive search algorithm for finding, in systematic form, rate R=\frac{1}{2} optimal-span 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.

Simplified convolutional self-doubly orthogonal codes: search algorithms and codes determination

A new class of convolutional self-doubly orthogonal codes which can be decoded by an iterative threshold decoder is presented. This new type of codes, called simplified convolutional self-doubly orthogonal codes (S-CSO2C), are obtained by simplifying some of the conditions on the double orthogonality of the convolutional self-doubly orthogonal codes (CSO2C). The relaxing of these conditions yields a substantial reduction of the total decoding delay induced by the memory length of the convolutional encoder at a cost of any a small degradation of the error performances. These simplified codes are also amenable to high coding rates R = b/(b + 1), b > 1 by puncturing a rate 1/2 systematic convolutional encoder. These new simplified CSO2C provide an interesting alternative for low complexity implementation error correcting schemes.

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

In this paper, we present new results on the search and determination of wide-sense convolutional self-doubly orthogonal codes (CSO/sup 2/C-WS) which can be decoded using a simple iterative threshold decoding algorithm without interleaving. For their iterative decoding, in order to ensure the independence of observables over the first two iterations without the presence of interleavers, these CSO/sup 2/C must satisfy specific orthogonal properties of their generator connections. The error performances of CSO/sup 2/C, depend essentially on the number of taps J of the code generators but not on the code memory length. Since the overall latency of the iterative threshold decoding process is proportional to the memory length of the codes, therefore, when searching for the best CSO/sup 2/C-WS of a given J value, the memory length of the codes should be chosen to be as small as possible. In this paper, we present a code-searching technique based on heuristic computer searching algorithms which have yielded the best known CSO/sup 2/C-WS. The construction method for CSO/sup 2/C-WS has provided the best known r=1/2 codes with the shortest memory length having J/spl les/30. Although not very complex to implement, the search method presented here is quite efficient especially in reducing very substantially the execution time required to determine the codes with the shortest spans. Furthermore, in addition to presenting the search results for the codes, error performances obtained by simulation are also provided.

High-Rate Punctured Convolutional Self-Doubly Orthogonal Codes for Iterative Threshold Decoding

The puncturing technique allows obtaining high-rate convolutional codes from low-rate convolutional codes used as mother codes. This technique has been successfully applied to generate good high-rate convolutional codes which are suitable for Viterbi and sequential decoding. In this paper, we investigate the puncturing technique for convolutional self-doubly orthogonal codes (CSO/sup 2/C) which are decoded using an iterative threshold-decoding algorithm. Based on an analysis of iterative threshold decoding of the rate-R=b/(b+1) punctured systematic CSO/sup 2/C, the required properties of the rate-R=1/2 systematic convolutional codes (SCCs) used as mother codes are derived. From this analysis, it is shown that there is no need for the punctured mother codes to respect all the required conditions, in order to maintain the double orthogonality at the second iteration step of the iterative threshold-decoding algorithm. The results of the search for the appropriate rate-R=1/2 SCCs used as mother codes to yield a large number of punctured codes of rates 2/3/spl les/R/spl les/6/7 are presented, and some of their error performances evaluated.

Iterative threshold decoding without interleaving for convolutional self-doubly orthogonal codes

A novel iterative error control technique based on the threshold decoding algorithm and new convolutional self-doubly orthogonal codes is proposed. It differs from parallel concatenated turbo decoding as it uses a single convolutional encoder, a single decoder and hence no interleaver, neither at encoding nor at decoding. Decoding is performed iteratively using a single threshold decoder at each iteration, thereby providing good tradeoff between complexity, latency and error performance.