Christian Cardinal

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.

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.

On the performance of interference cancellation in wireless ad hoc networks

This letter presents a novel approach for deriving a lower bound on the outage probability of interference cancellation receiver in ad hoc networks for a class of channel fading. Our approach is based on the following observation: under the power decay law model for large-scale fading with an exponent ¿ strictly greater than 2, the sum of the interferences at a receiver has the same order as the strongest signal. This feature still holds when the small-scale fading has a finite 2/¿-fractional moment. This fact is used to develop an approximation which is also a compact lower bound on the outage probability.

Turbo decoding using convolutional self doubly orthogonal codes

In this paper we present a novel iterative error control technique which circumvents both the complexity and latency shortcomings of the usual turbo codes. It differs from usual turbo coding techniques as it uses a single encoder (hence with no interleaver at the encoding process) and a single decoder. The technique is based on a novel class of orthogonal threshold decodable codes called convolutional self doubly orthogonal codes (CSO/sup 2/C).

A New Approach for the Construction of Powerful LDPC Convolutional Codes

A novel approach for the algebraic construction of low-density parity-check (LDPC) convolutional codes is presented. It is based on the orthogonality structures of the codes. The proposed code construction leads to a girth of at least 10 in the Tanner graph. The error performance of these codes compares favorably with the usual LDPC convolutional codes, especially at low signal-to-noise ratio range.

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.

Forward-only iterative decoding of convolutional self-orthogonal codes

A class of forward-only iterative belief propagation algorithms for decoding convolutional self-orthogonal codes is presented, which perform successively a number of one-step decoding and thus have only an initial decoding delay. The one-step belief propagation decoders can be realized in a similar way to one-step threshold decoders. The error performance of the algorithms is easily improved by using a weighing technique. These iterative algorithms allow good tradeoffs between complexity, latency, and error performance of the coding scheme.

A serial design of iterative belief propagation decoders for convolutional codes

The belief propagation (BP) decoding algorithm may be suitable for the decoding of convolutional self-orthogonal codes which were originally proposed for one-step threshold de- coding. In this paper, a serial design of iterative BP decoder for convolutional self-orthogonal codes is presented. Using the alge- braic structures of convolutional codes, the iterative BP decoder is designed as a serial concatenation of several one-step BP de- coders. These one-step BP decoders are implemented using mainly the shift registers in a structure similar to that of type-II threshold decoders. The iterative BP decoder performs a non- trellis-based forward-only algorithm and has only an initial de- coding delay, thus avoiding intermediate decoding delays that usually accompany BP or turbo decoding of data frames. As shown by simulation results, the use of weighing techniques has provided substantial improvements to the error performance of the iterative BP decoding at a cost of several multipliers in hard- ware implementation. The iterative BP decoder may be attrac- tive to the practical applications in very high data rate areas.

Convolutional self doubly orthogonal codes for iterative decoding without interleaving

We present a novel turbo error control technique which circumvents both the complexity and latency shortcomings of the usual turbo codes. It differs from usual turbo coding techniques as if uses single encoder and a single decoder. The technique is based on a novel class of orthogonal threshold decodable codes called convolutional self doubly orthogonal codes (CSO/sup 2/C) which do not require interleaving.

Reduced-Complexity Convolutional Self-Doubly Orthogonal Codes for Efficient Iterative Decoding

A variant of convolutional self doubly orthogonal codes that can be decoded using an iterative threshold decoding algorithm is presented. These new codes are called degenerate convolutional self-doubly orthogonal codes since not all the double orthogonality conditions required to obtained convolutional self doubly orthogonal codes defined in the wide sense are satisfied. The memory lengths or spans of the degenerate convolutional self-doubly orthogonal codes are substantially shorter than those of the usual convolutional self doubly orthogonal codes defined in the wide sense, at the cost of only a slight degradation of the error performances. As a consequence, very low complexity implementations are possible with these error correcting schemes. Several new degenerate convolutional self doubly orthogonal codes have been determined and their error performances evaluated using computer simulations