In this paper, the problem of maximizing the mutual information of independent parallel Gaussian-noise channels is studied under an average power constraint with one-bit analog-to-digital (A/D) convertor. It is shown that the power allocation problem is a convex optimization problem, which can be solved efficiently. Meanwhile, the waterfilling interpretation for the power allocation problem is also given. Further, the combined 1bit/dimension vector quantizer and precoder design are studied in the 2 parallel independent channels. Simulation results demonstrate that substantial gain can be achieved compared to power allocation scheme especially when the difference of channel gains is large and the range of SNR is low to medium. Introduction The problem of power allocation among a bank of independent parallel channels has drawn a great deal of attention. For a given independent parallel channels under a total power constraint, it is well known that Gaussian inputs with the waterfilling power allocation scheme will achieve the capacity [1]. However, Gaussian inputs can never be realized in practice due to its infinite peak-to-average ratios. As a consequence, discrete constellations such as phase shift keying (PSK) and quadrature amplitude modulation (QAM) are adopted in practical communication systems. In [2], the power allocation for parallel Gaussian channels with arbitrary input distributions is investigated. The optimum is ensured to be found and has a good interpretation named mercury/waterfilling. In addition, it has been demonstrated that a linear precoder may increase the mutual information between the source and channel’s output. Thus the optimal precoder is designed in parallel Gaussian channels with arbitrary inputs [3]. The above works perform the design by assuming that the precision of the analog-to-digital converter (ADC) is infinite. Traditionally, the precision of the ADC is often high enough (e.g., 10-12 bits or more), which makes the assumption of the infinite precision of the ADC practical. Consequently, considerable effort is spent on the optimization of modulation, demodulation and decoding [4,5]. However, as the data rates increases, high-speed high-precision ADC is often not available. Even it is available, the cost and power dissipation are large [6]. One approach is to decrease the resolution of an ADC to a few bits by reducing the number of comparators. As a result, the receiver blocks such as synchronization, channel estimation and demodulation need to be redesigned [7],[8],[9]. In addition, the quantizer must be designed carefully in order to reduce the performance loss compared to the case of high precision ADC. There has been a lot of work focusing on the performance limits of low precision quantization ranging from signal processing to communication theory. The problem of estimating a frequency of a single complex-valued sinusoid in additive Gaussian noise for 1bit quantization is studied, which demonstrates that the performance degradation is not large [10]. In [11], a scheme is proposed to estimate the impulse response of a dispersive channel when a low precision ADC utilized at the receiver. It is shown that the scheme provides performance close to that of the full precision sampling. The capacity of the additive white Gaussian noise (AWGN) channel with low-precision (e.g., 1-4 bits) receiver is studied in [12]. It is demonstrated that at high enough signal to noise ratio (SNR), the low-precision receiver incus a small loss compared to unquantized observations. This motivates us to study the capacity of the independent parallel channels with low-precision ADC. In this paper, we first consider the capacity of the independent parallel channels under a total power constraint with one bit ADC. Then a precoder is proposed to a specific two independent International Conference on Information Sciences, Machinery, Materials and Energy (ICISMME 2015) © 2015. The authors Published by Atlantis Press 25 parallel channels, and a 1bit/dimension vector quantizer is utilized. It is shown that this precoder scheme works better than the power allocation method, especially when the SNR is medium and the difference of the channel gain is large. Preliminary In this paper, we first review the classical n parallel independent channels model snr 1 i i i i i y h p x n i n = + , = , ,  , (1) where i y , i h , i p and i x denote respectively the i th output, channel coefficient, power and input, snr is the signal to noise ratio, ~ (0 1) i n N , denotes the i.i.d. additive Gaussian noise. We assume that each i x is independent of each other and is a zero-mean unit variance random variable, and 1 { } n i i p = satisfy 1 1 n i i p = = ∑ . Although Gaussian inputs will achieve the channel capacity, we assume that the input 1 { } i i x = is always drawn equiprobable from an M-ary alphabet in this paper. Consequently, the mutual information expression 1 ( { } ) n i i I p = , | x y which involves Gaussian kernel integration can be obtained. With the established relationship between the mutual information and the minimum mean square error (MMSE), one can obtain the optimal power allocation scheme [2]. Linear precoder can be utilized to increase the mutual information between the input and output with finite alphabet input, i.e., by allowing the transmitter and receiver to cooperate in communicating and decoding. By defining 1 diag( ) n h h = , , H  as the channel matrix, T 1 [ ] n y y = , , y  as the n outputs, n n R × ∈ P as the precoder which is designed, the mathematical model is snr = + y HPx n . (2) To find the optimal precoder ∗ P , the fixed point iteration T 1 snr k k k e n     +   = Π + Σ P P H HP is adopted [3], where k denotes the iteration index, n is a fixed small step size, e Σ is a MMSE matrix and ( ) Π ⋅ is an operation that enforces the variable to have unite Frobenius norm. Note that both the MMSE matrix e Σ and mutual information ( ) I , | x y P are computed using Gaussian Hermite quadrature rules [13]. Power allocation under 1bit quantization We first consider the case that power allocation is only adopted with the receiver using one-bit analog-to-digital (A/D) convertor. For the power allocation problem, model (1) reduces to be sign snr 1 i i i i i y h p x n i n         = + , = , , .  (3) The input-output mutual information on the i th channel is denoted as ( ) ( ) i i i i i I p I x y = ; . The capacity of the i th channel is the supreme of the mutual information taken over all possible input distributions