This study deals with two linear precoders: the maximization of the minimum Euclidean distance between received symbol-vectors, called here max-dmin, and the maximization of the post-processing signal-to-noise ratio termed max-SNR or beamforming. Both have been designed for reliable MIMO transmissions operating over uncorrelated Rayleigh fading channels. Here, we will explain why performances in terms of bit error rates show a significant enhancement of the max-dmin over the max-SNR whenever the number of antennas is increased. Then, from theoretical developments, we will demonstrate that, like the max-SNR precoder, the max-dmin precoder achieves the maximum diversity order, which is warrant of reliable transmissions. The current theoretical knowledge will be applied to the case-study of a system with two transmit- or two receive-antennas to calculate the probability density functions of two channel parameters directly linked to precoder performances for uncorrelated Rayleigh fading channels. At last, this calculation will allow us to quickly get the BER of the max-dmin precoder further to the derivation of a tight semi-theoretical approximation.

In this paper, we discuss the performance and computational complexity of modulo-type Viterbi decoder (MVD) for high-speed digital transmission applications. It is shown that the MVD, which is a combination of modulo operation and Viterbi decoder at the receiver, has the same performance as a conventional Viterbi decoder (CVD) with extended constellations. We also show by complexity analysis that the MVD in conjunction with the Tomlinson-Harashima (TH) precoder at the transmitter reduces the system complexity significantly as compared to the CVD. The performance of the digital subscriber line (xDSL) system employing the MVD is investigated in the presence of near-end crosstalk (NEXT) and impulsive noise.

In this paper, we propose a new kind of precoding method, modulated coded vector-TH precoding, to mitigate the channel intersymbol interference. The optimal design of the modulated code in vector TH precoding is presented. The coding gain of modulated coded vector TH precoding over conventional scalar TH precoding scheme is investigated in theory. Some simulation results are reported, which show that the proposed modulated coded vector TH scheme can provide a considerable coding gain compared with the conventional precoding techniques.