Catherine Douillard

Turbo codes with rate-m/(m+1) constituent convolutional codes

The original turbo codes (TCs), presented in 1993 by Berrou et al., consist of the parallel concatenation of two rate-1/2 binary recursive systematic convolutional (RSC) codes. This paper explains how replacing rate-1/2 binary component codes by rate-m/(m+1) binary RSC codes can lead to better global performance. The encoding scheme can be designed so that decoding can be achieved closer to the theoretical limit, while showing better performance in the region of low error rates. These results are illustrated with some examples based on double-binary (m=2) 8-state and 16-state TCs, easily adaptable to a large range of data block sizes and coding rates. The double-binary 8-state code has already been adopted in several telecommunication standards.

Computing the minimum distance of linear codes by the error impulse method

A new method for computing the minimum distances of linear error-correcting codes is proposed and justified. Unlike classical techniques that rely on exhaustive or partial enumeration of codewords, this new method is based on the ability of the Soft-In decoder to overcome Error Impulse input patterns. It is shown that the maximum magnitude of the Error Impulse that can be corrected by the decoder is directly related to the minimum distance. This leads to a very fast algorithm to obtain minimum distances of any linear code whatever the block size and the code rate considered. In particular, the method can be advantageously worked out for turbo-like concatenated codes.

An overview of turbo codes and their applications

More than ten years after their introduction, turbo Codes are now a mature technology that has been rapidly adopted for application in many commercial transmissions systems. This paper provides an overview of the basic concepts employed in convolutional and block turbo codes, and review the major evolutions in the field with an emphasis on practical issues such as implementation complexity and high-rate circuit architectures. We address the use of these technologies in existing standards and also discuss future potential applications for this error-control coding technology

Adaptive Trace-Orthonormal STBC for MIMO System with Capacity Approaching FEC Codes

Space time block codes (STBCs) are commonly designed according to the rank-determinant criteria, suitable for high signal to noise ratio (SNR) values. However, capacity approaching forward error correcting codes, used in practical communication systems, achieve iterative convergence at low to moderate SNR. In this paper we first present a non- asymptotic STBC design criterion based on the bitwise mutual information (BMI) maximization at a specific target SNR. According to this BMI criterion, we then optimize a trace-orthonormal- based STBC structure. Therefore, designed STBC becomes adaptive with respect to the SNR. Proposed adaptive trace-orthonormal STBC shows identical or better performance than 2×2 STBCs of a turbo-coded WiMAX system.

Low ML-detection complexity, adaptive 2×2 STBC, with powerful FEC codes

We present an adaptive space time block code (STBC) for 2×2 MIMO systems designed to be used with powerful forward error correcting (FEC) codes and having a low ML-detection complexity. STBCs are commonly designed according to the rank-determinant criteria, suitable for high signal to noise ratio (SNR) values. However, powerful FEC codes like turbo codes achieve iterative convergence at low to moderate SNR. Thus, we first propose a non-asymptotic STBC design criterion based on the bitwise mutual information (BMI) maximization at a specific target SNR. According to this criterion, an adaptive matrix D based STBC is defined for a wide range of SNRs. Resulting code outperforms the original matrix D and closes the gap to the more complex Golden code in the context of a WiMAX system.