Nonlinear codes for multiple access to binary channels and higher-order modulations over the AWGN channel

First, this work proposes an Interleave-Division Multiple Access (IDMA)-based architecture with single-user decoding to allow uncoordinated multiple access to binary-input binary-output multiple-access channels (BIBO-MAC), in particular the OR multiple access channel and OR with cancellations (ORC-MAC). These channels can be used as models for optical channels. Over the OR-MAC 70% of full efficiency can be achieved with this architecture. Full capacity can be only achieved by providing a low ones density in transmission, which requires the use of nonlinear codes.;First, nonlinear trellis codes (NLTC) are considered. Design criteria for NLTC codes with a controlled ones density are introduced. Tight analytical bounds on their performance over the Z-Channel are presented. Also, an improved Bhattacharyya bounding technique for decoding error probability is shown that applies to any channel. This new bound is tighter than the Bhattacharyya bound as presented in textbooks by a factor of 1/2. An analysis on the performance of these codes in the BIBO-MAC for large number of users depending on the number of states of the trellis is shown. This tool provides a means to decide the proper number of states of the trellis. In the OR-MAC case, with a serial concatenation of nonlinear trellis codes and a high rate Reed-Solomon code, 30% of efficiency (or 43% of the available capacity given single-user decoding) is achieved with a bit error rate in the order of 10-10 for any number of users. For a particular case of the ORC-MAC, the OR channel with coherent interference, an efficiency of 20% (or 29% of the available capacity given single-user decoding) is achieved.;In order to provide low error probability at rates close to capacity, nonlinear turbo codes are proposed in this work. For nonlinear turbo codes, two applications are considered: the transmission of 8PSK over the AWGN channel and the uncoordinated multiple access to the BIBO-MAC using IDMA with single user decoding.;For the first application, parallel concatenated trellis coded modulations have been traditionally designed using concatenated linear convolutional codes and a bit-to-constellation-point mapper. We show that this encoder structure is suboptimal under certain scenarios, and that nonlinear turbo coded modulation can improve the performance. As an example, we design a rate-2 bits/s/Hz 16-state nonlinear turbo code for 8PSK, which outperforms the best previously reported linear turbo code with labeling by 0.2 dB over AWGN under same conditions. This code is within 0.42 dB away from capacity at a BER = 10-5.;For the second application, nonlinear turbo codes are designed for the Z-channel, along with an IDMA-based architecture that allows uncoordinated multiple access in the OR-MAC. Simulation results show a BER below 10 -6 with 8 states for up to 24 users, with an efficiency of 60% (or 87% of the available capacity given single-user decoding) and an interleaver length of 8192 bits. Also, an analysis on the limitation on the number of users, for a certain complexity, sum-rate and BER is shown. For a number of users between 24 and 44, a 16-state nonlinear turbo code is used to maintain a good performance.;To predict the performance of these nonlinear turbo codes, an extension of Benedetto's uniform interleaver analysis for nonlinear constituent codes is derived. It is shown that the design criteria for linear codes can be generalized to nonlinear codes. In particular, we generalize the notion of effective free distance for nonlinear constituent codes, and conclude that this is an important parameter to maximize at the design stage of nonlinear codes as well as linear codes.;Finally, the design of arbitrarily low-rate turbo codes is considered. We propose an optimization criteria and reduce the turbo-design problem to the design of block codes for the assignment of output sequences to the trellis branches of the constituent encoders. We show that BCH codes concatenated with repetition codes are optimal for labeling. Moreover, we show that for a fixed number of trellis states these codes achieve arbitrarily low rates, and hence arbitrarily low SNRs, with practically the same performance in terms of Eb/N0. Simulation results are shown for 8-state and 16-state turbo codes with rates as low as 1/505. The 16-state rate 1/505 turbo code with an interleaver-length of 8192 provides a BER ≃ 10-5 at an SNR ≃ --27.6 dB (Eb/N 0 --0.55 dB), around 1dB away from the ultimate low-rate Shannon limit. (Abstract shortened by UMI.)...