EXIT charts for system design and analysis

Near-capacity performance may be achieved with the aid of iterative decoding, where extrinsic soft information is exchanged between the constituent decoders in order to improve the attainable system performance. Extrinsic information Transfer (EXIT) charts constitute a powerful semi-analytical tool used for analysing and designing iteratively decoded systems. In this tutorial, we commence by providing a rudimentary overview of the iterative decoding principle and the concept of soft information exchange. We then elaborate on the concept of EXIT charts using three iteratively decoded prototype systems as design examples. We conclude by illustrating further applications of EXIT charts, including near-capacity designs, the concept of irregular codes and the design of modulation schemes

Turbo codes and turbo algorithms

In the first part of this paper, several basic ideas that prompted the coming of turbo codes are commented on. We then present some personal points of view on the main advances obtained in past years on turbo coding and decoding such as the circular trellis termination of recursive systematic convolutional codes and double-binary turbo codes associated with Max-Log-MAP decoding. A novel evaluation method, called genieinitialised iterative processing (GIIP), is introduced to assess the error performance of iterative processing. We show that using GIIP produces a result that can be viewed as a lower bound of the maximum likelihood iterative decoding and detection performance. Finally, two wireless communication systems are presented to illustrate recent applications of the turbo principle, the first one being multiple-input/multiple-output channel iterative detection and the second one multi-carrier modulation with linear precoding

Precoded BICM design for MIMO transmit beamforming and associated low-complexity algebraic receivers

Abstract-In this paper, we design bit interleaved coded modulations including a partial algebraic precoder in order to transmit several spatial streams with full diversity over a transmit beamformed MIMO channel. The achievable diversity orders with the coded modulation are derived, and allow for efficiently choosing the system parameters for optimizing the performance. Additionnally, a very efficient low complexity soft output detector based on algebraic reduction is presented. With a low complexity at the receiver, the precoded BICM system allows achieving high performance at very high efficiencies, e.g., 12 bits per second per hertz. I. INTRODUCTION The new standards of wireless communications, e.g., 802.11n and 3GPP-LTE, include a variety of techniques for transmitting over mutliple antenna channels: Spatial-division multiplexing, space-time block coding, transmit beamforming, and so on. A trade-off between data rate, range, mobility and receiver complexity can be achieved by a relevant choice of the transmission technique. In this paper, we focus on low mobility users and transmit beamforming techniques. For low and average spectral efficiencies, the MIMO channel capacity can be maximized by transmitting on the best eigenvalue of the channel realization and can be further improved by applying water-filling techniques In section II, we present the channel model and notations. In section III, the equivalent channels as seen by the decoder input and including a partial precoder are described, while achievable bounds on the diversity for these channels are derived in section IV. These bounds are used to choose the optimal size of the partial algebraic precoder. In section V, w

CROSSTALK-RESILIANT CODING FOR HIGH DENSITY DIGITAL RECORDING

Increasing the track density in magnetic systems is very difficult due to inter-track interference (ITI) caused by the magnetic field of adjacent tracks. This work presents a two-track partial response class 4 magnetic channel with linear and symmetrical ITI; and explores modulation codes, signal processing methods and error correction codes in order to mitigate the effects of ITI. Recording codes were investigated, and a new class of two-dimensional run-length limited recording codes is described. The new class of codes controls the type of ITI and has been found to be about 10% more resilient to ITI compared to conventional run-length limited codes. A new adaptive trellis has also been described that adaptively solves for the effect of ITI. This has been found to give gains up to 5dB in signal to noise ratio (SNR) at 40% ITI. It was also found that the new class of codes were about 10% more resilient to ITI compared to conventional recording codes when decoded with the new trellis. Error correction coding methods were applied, and the use of Low Density Parity Check (LDPC) codes was investigated. It was found that at high SNR, conventional codes could perform as well as the new modulation codes in a combined modulation and error correction coding scheme. Results suggest that high rate LDPC codes can mitigate the effect of ITI, however the decoders have convergence problems beyond 30% ITI

Error-rate in Viterbi decoding of a duobinary signal in presence of noise and distortions: theory and simulation

The Viterbi algorithm, presented in 1967, allows a maximum likelihood de- coding of partial response codes. This study focuses on the duobinary code which is the first member of this family and has been specified for the digital part of television systems recommended by International Organizations. Up to now the error-rate, which is the main criterion of the performance, has been evaluated by simulation. Although there exist the- oretical bounds, these bounds are not satisfactory for a channel such as broadcasting (by terrestrial transmitters, cable networks or satellite) which is strongly impaired by noise, and linear and non-linear distortions. Analytical methods, verified by simulation, are presented here in order to evaluate the theoretical and exact values of the error-rate, in the form of series of numerical integrations, for a transmission in baseband or in radio-frequency with quadriphase modulation (or AM/VSB for cable networks) and coherent demodulation, in presence of noise and several distortions. This methodology can be later extended to other partial response codes, to convolutional codes and their concatenations

Error control techniques for satellite and space communications

Shannon's capacity bound shows that coding can achieve large reductions in the required signal to noise ratio per information bit (E sub b/N sub 0 where E sub b is the energy per bit and (N sub 0)/2 is the double sided noise density) in comparison to uncoded schemes. For bandwidth efficiencies of 2 bit/sym or greater, these improvements were obtained through the use of Trellis Coded Modulation and Block Coded Modulation. A method of obtaining these high efficiencies using multidimensional Multiple Phase Shift Keying (MPSK) and Quadrature Amplitude Modulation (QAM) signal sets with trellis coding is described. These schemes have advantages in decoding speed, phase transparency, and coding gain in comparison to other trellis coding schemes. Finally, a general parity check equation for rotationally invariant trellis codes is introduced from which non-linear codes for two dimensional MPSK and QAM signal sets are found. These codes are fully transparent to all rotations of the signal set