Instead of a random interleaver, an algebraic interleaver interconnecting two simple convolutional codes with feedback encoders forms an algebraic quasi-cyclic code. An (nC , k) convolutional code in tailbiting form becomes a quasi-cyclic (QC) linear code of length LnC for some L = Mn. Interleavers with a period M connect two such codes to produce a QC turbo code. The QC turbo codes check equat...

We track the density of extrinsic information in iterative turbo decoders by actual density evolution, and also approximate it by consistent Gaussian density functions. The approximate model is verified by experimental measurements. We view the evolution of these density functions through an iterative decoder as a nonlinear dynamical system with feedback. Iterative decoding of turbo codes and o...

—This article presents an FPGA implementation of an ultra-high-speed Reed-Solomon (RS) turbo decoder. A performance analysis is performed showing that RS Block Turbo Codes (RS-BTC) have decoding performance equivalent to Bose Ray-Chaudhuri Hocquenghem-Block Turbo Codes (BCH-BTC). A ratio between the decoder throughput and the decoder area is used to show the higher ef ciency of the RS full para...

This paper is concerned with a family of concatenated tree (CT) codes. CT codes are special low-density paritycheck (LDPC) codes consisting of several trees with large spans. They can also be regarded as special turbo codes with hybrid recursive/nonrecursive parts and multiple constituent codes. CT codes are decodable by the belief-propagation algorithm. They combine many advantages of LDPC and...

Bit interleaved coded modulation employing asymmetric turbo codes is investigated. An asymmetric turbo code uses two different constituent codes. The benefit of using different constituent codes is that they may complement each other during iterative decoding of the asymmetric turbo code. This can be visualized using the input-output extrinsic information transfer (EXIT) chart based on mutual i...

This paper proposes a class of full space diversity full rate space-time turbo codes. Both parallel concatenated and serially concatenated codes are designed. The full space diversity design is facilitated by a rank theory. Compared with space-time trellis codes, the simulations show the space-time turbo codes have excellent performance in both quasi-static fading channels and time varying fadi...

We define analog product codes as a special case of analog parallel concatenated codes. These codes serve as a tool to get some more insight into the convergence of “Turbo” decoding. We prove that the iterative “Turbo”-like decoding of analog product codes indeed is an estimation in the least-squares sense and thus correspond to the optimum maximum-likelihood decoding.

Reliable wireless broadcast with asynchronous data access based on fountain coding is investigated. We review the traditional problem formalization for fountain codes operating on erasure channels and we generalize the problem formalization to arbitrary types of channels. We introduce a novel type of rateless codes based on the turbo principle: the Turbo-Fountain. The TurboFountain is able to c...