S. ten Brink

Convergence behavior of iteratively decoded parallel concatenated codes

Mutual information transfer characteristics of soft in/soft out decoders are proposed as a tool to better understand the convergence behavior of iterative decoding schemes. The exchange of extrinsic information is visualized as a decoding trajectory in the extrinsic information transfer chart (EXIT chart). This allows the prediction of turbo cliff position and bit error rate after an arbitrary number of iterations. The influence of code memory, code polynomials as well as different constituent codes on the convergence behavior is studied for parallel concatenated codes. A code search based on the EXIT chart technique has been performed yielding new recursive systematic convolutional constituent codes exhibiting turbo cliffs at lower signal-to-noise ratios than attainable by previously known constituent codes.

Achieving near-capacity on a multiple-antenna channel

Recent advancements in iterative processing of channel codes and the development of turbo codes have allowed the communications industry to achieve near-capacity on a single-antenna Gaussian or fading channel with low complexity. We show how these iterative techniques can also be used to achieve near-capacity on a multiple-antenna system where the receiver knows the channel. Combining iterative processing with multiple-antenna channels is particularly challenging because the channel capacities can be a factor of ten or more higher than their single-antenna counterparts. Using a list version of the sphere decoder, we provide a simple method to iteratively detect and decode any linear space-time mapping combined with any channel code that can be decoded using so-called soft inputs and outputs. We exemplify our technique by directly transmitting symbols that are coded with a channel code; we show that iterative processing with even this simple scheme can achieve near-capacity. We consider both simple convolutional and powerful turbo channel codes and show that excellent performance at very high data rates can be attained with either. We compare our simulation results with Shannon capacity limits for ergodic multiple-antenna channel.

Design of low-density parity-check codes for modulation and detection

A coding and modulation technique is studied where the coded bits of an irregular low-density parity-check (LDPC) code are passed directly to a modulator. At the receiver, the variable nodes of the LDPC decoder graph are connected to detector nodes, and iterative decoding is accomplished by viewing the variable and detector nodes as one decoder. The code is optimized by performing a curve fitting on extrinsic information transfer charts. Design examples are given for additive white Gaussian noise channels, as well as multiple-input, multiple-output (MIMO) fading channels where the receiver, but not the transmitter, knows the channel. For the MIMO channels, the technique operates within 1.25 dB of capacity for various antenna configurations, and thereby outperforms a scheme employing a parallel concatenated (turbo) code by wide margins when there are more transmit than receive antennas.

Extrinsic information transfer functions: model and erasure channel properties

Extrinsic information transfer (EXIT) charts are a tool for predicting the convergence behavior of iterative processors for a variety of communication problems. A model is introduced that applies to decoding problems, including the iterative decoding of parallel concatenated (turbo) codes, serially concatenated codes, low-density parity-check (LDPC) codes, and repeat-accumulate (RA) codes. EXIT functions are defined using the model, and several properties of such functions are proved for erasure channels. One property expresses the area under an EXIT function in terms of a conditional entropy. A useful consequence of this result is that the design of capacity-approaching codes reduces to a curve-fitting problem for all the aforementioned codes. A second property relates the EXIT function of a code to its Helleseth-Klove-Levenshtein information functions, and thereby to the support weights of its subcodes. The relation is via a refinement of information functions called split information functions, and via a refinement of support weights called split support weights. Split information functions are used to prove a third property that relates the EXIT function of a linear code to the EXIT function of its dual.

Design of repeat-accumulate codes for iterative detection and decoding

Extrinsic information transfer (EXIT) charts are used to design systematic and nonsystematic repeat-accumulate (RA) codes for iterative detection and decoding. The convergence problems of nonsystematic RA codes are solved by introducing a biregular, or doped, layer of check nodes. As examples, such nonsystematic codes are designed for multi-input/multi-output (MIMO) fading channels and are shown to operate close to capacity.

A close-to-capacity dirty paper coding scheme

The writing on dirty paper-channel model offers an infor- mation theoretic framework for precoding techniques for canceling arbi- trary interference known at the transmitter. Using lattice strategies and MMSE scaling, lossless precoding is theoretically possible at any signal to noise-ratio. Following this approach, we design an end-to-end coding real- ization of a system materializing a significant portion of the promised gains. We employ vector quantization in combination with iterative decoding of capacity-approaching codes to achieve more than 2dB improvement over the best scalar quantization scheme. Code design is done using the EXIT chart technique.

Code rate and the area under extrinsic information transfer curves

Extrinsic information transfer (EXIT) charts predict the convergence behavior of iterative decoding and detection schemes. The EXIT analysis is made precise by introducing a model that applies to iterative decoding of parallel concatenated, serially concatenated, and low-density parity-check codes. The model leads to an area property of EXIT charts.

Code doping for triggering iterative decoding convergence

The paper describes inner and outer code doping to enable iterative decoding of serially concatenated codes (SCC) which use inner rate one recursive convolutional codes of memory greater than one.The paper describes inner and outer code doping to enable iterative decoding of serially concatenated codes (SCC) which use inner rate one recursive convolutional codes of memory greater than one.

Detection thresholds of iterative MIMO processing

This paper studies threshold effects of iterative detection and decoding on multiple input/multiple output (MIMO) channels using the extrinsic information transfer (EXIT) chart technique.

Convergence of multidimensional iterative decoding schemes

We study the iterative decoding convergence of parallel concatenated codes (PCC) consisting of three constituent codes. A three-dimensional extension of the extrinsic information transfer (EXIT) chart technique is used to predict convergence thresholds and to visualize the course of the iteration.