As a generalization of the binary spreading scheme in conventional direct-sequence code-division multiple-access (DS-CDMA) and interleave-division multiple-access (IDMA), a finite field spreading scheme is proposed for a synchronous multiple-access channel (MAC) with Gaussian noise and equal-power users. For each user, each information symbol over a finite field is spread into a length-L field vector by L-field multiplications. At the receiver, an iterative multi-user decoding algorithm on a factor graph is developed to recover each user's information symbol. To estimate the bit error rate performance of an uncoded finite field spreading system, an extrinsic information transfer analysis of the finite field despreading is given. This analysis shows that in addition to overcoming multi-user interference, the finite field spreading scheme can also provide an additional coding gain to overcome Gaussian noise compared with the conventional spreading scheme. This coding gain increases with the field order. The finite field spreading serially concatenated with a nonbinary low-density parity-check (LDPC) code, with field order 64, approaches the MAC capacity within 0.26 dB at a sum rate of 0.25.

A k-user parallel concatenated code (PCC) is proposed for a Gaussian multiple-access channel with symbol synchronization and equal power users. In this code, each user employs a PCC with M + 1 component codes, where the first component code is a rate 1/q repetition code and the other M component codes are the same rate-1 convolutional code 1/1+D. The K-user PCC achieves a larger maximum sum rate, at the high rate region, than the conventional scheme of an error correction code serially concatenated with a spreading.

We propose a generalized construction scheme of error-correcting signature code. We form a signature matrix whose rows become the non-zero codewords of the signature code. In the coding scheme, a signature matrix is obtained from a Hadamard matrix by replacing every element by an initial signature matrix or its associated matrix depending on the element's binary value. The proposed code has longer length, higher decodability, and larger cardinality. In this coding scheme, the initial signature matrix is in a general form and can be a signature matrix of any initial signature code. Different initial matrices provide different error-correcting signature codes, including conventional codes. This general form makes it possible to obtain error-correcting signature codes with a higher sum rate than conventional codes.

As a generalization of the binary coding-spreading scheme, nonbinary coding-spreading scheme is proposed for a synchronous binary-input multiple-access channel (MAC) with Gaussian noise, equal-power, and equal-rate users. In this scheme, each user employs the same nonbinary low-density parity-check code serially concatenated with a nonbinary low-rate mapping, referred to as nonbinary spreading. A user-specific interleaving is employed to make the transmitted data of each user random-like. It is shown that the iterative multi-user decoding threshold of nonbinary coding-spreading scheme is less than 0.5 dB away from the MAC capacity at many sum rates.

A multi-user repeat-accumulate interleave-division (RAID) system is considered for a multiple-access channel (MAC) with binary inputs, equal-power, and symbol synchronization. In the system, a regular repeat-accumulate (RA) code serially concatenated with block spreading is employed for each user. At the receiver, multi-user message-passing decoding is performed on a single factor graph. Over the MAC with additive white Gaussian noise (AWGN), a fixed point analysis is developed to obtain the optimal code rate and the spreading length that give the maximum sum rate for an arbitrary small decoding error rate.

The necessary and sufficient condition of the channel capacity is rigorously formulated for the$N$-user discrete memoryless multiple-access channel (MAC). The essence is to invoke anelementaryMAC where sizes of input alphabets are not greater than the size of output alphabet. The main objective is to demonstrate that the channel capacity of an MAC is achieved by an elementary MAC included in the original MAC. The proof is quite straightforward by the very definition of the elementary MAC. The second objective is to prove that the Kuhn–Tucker conditions of the elementary MAC are sufficient (obviously necessary) for the channel capacity. The latter proof requires two distinctive properties of the MAC: Every solution of the Kuhn–Tucker conditions is a local maximum on the domain of all possible input probability distributions (IPDs), and then particularly for the elementary MAC a set of IPDs for which the value of the mutual information is not smaller than the arbitrary positive number is connected on the domain. As a result, in respect of the channel capacity, the MAC in general can be regarded as an aggregate of a finite number of elementary MACs.

A method for full-azimuth DoA estimation of multiple signals with a hexagonal array is proposed. The DoA estimation is performed in two steps. In the first, a set of estimate candidates is constructed by gathering the estimates that are obtained from applying the Unitary-ESPRIT algorithm to several translational invariances designed into a hexagonal array. In the second step, the DoA estimates are successively selected from the estimate candidate set by using a selection function. The proposed method removes the north-or-south signal membership ambiguity and the limitation on the number of estimable sources, problems common to any ESPRIT-based algorithm used with one translational invariance. Therefore, up to M - 1 signal DoA estimations can be expected with an M-element hexagonal array in the full azimuth. The successive-selection approach is based on a selection function that uses an estimate of the signal's spatial correlation matrix to successively select the DoA estimates. For each DoA estimate selection, the already estimated signal components are removed from the correlation matrix. The method's DoA estimation and resolution capabilities are demonstrated by computer simulation.

Error-correcting non-binary signature code is proposed. A 2j-1-decodable (k + 1)-ary signature code with code length 2j- 1 is recursively constructed. The code is used to identify users through a multiple-access adder channel, even in the presence of channel noise.

User identification by signature code is considered for noisy multiple-access adder channel. An n/2-decodable signature code is developed from a Hadamard matrix of order n. The code is used to identify users through the multiple-access adder channel even in the presence of channel noise. A decoding rule is provided to correct lfloor(n/2 - 1)/2rfloor errors and then to identify users

The necessary and sufficient condition for constructing a spreading set with decodability is investigated. It is proved that for a given ${\delta}$ -decodable spreading set and a $q \times q$ square matrix $H$ with components $1$ or $-1$ , a ${q\delta}$ -decodable spreading set $S^\ast$ is obtained if and only if $H$ is a Hadamard matrix. In addition, a decoding rule with error correction and message data detection is provided.

Error-correcting signature code is proposed. An n/2-decodable signature code with code length n - 1 and cardinality n - 1 is developed from an Hadamard matrix of order n. The code is used to identify users through the multiple-access adder channel, even in the presence of channel noise

This paper investigates the channel configuration of multiple-access channel (MAC) by decomposing the MAC into finite subMAC and also proves that there exists an input probability that achieves boundary of a capacity region and the total capacity of the original MAC.

Multiuser k-ary coding is proposed for a noisy multiple-access adder channel. It is shown that when a T-user /spl delta/-decodable k-ary code C is given a priori, a qT-user /spl lambda//spl delta/-decodable k-ary code C/sup */ is obtained by using a matrix, such as a Hadamard matrix or a conference matrix of order q, where /spl lambda/ is a positive integer depending on the matrix. More noteworthy is that the code C is an arbitrary /spl delta/-decodable k-ary code, and that the coding scheme preserves the total rate, i.e., the total rate of C/sup */ is equal to that of C.

The total capacity is evaluated for an arbitrary two-user multiple-access channel (MAC) with a binary output. The basic idea is to subdivide the MAC into a finite number of elementary MACs, i.e., a two-user MAC with binary inputs and binary outputs. These elementary MACs are classified further into two cases by the type of channel matrix. For each case, a necessary and sufficient condition of the total capacity is established by partially converting the ordinary Kuhn-Tucker condition. The solution of the necessary and sufficient condition determines the optimal distribution that achieves the total capacity of the elementary MAC. Then, for the arbitrary two-user MAC, it is shown that the total capacity is determined by evaluating the finite number of total capacities for those elementary MACs. An iteration procedure is proposed to calculate the total capacity of the MAC.

Given a graph G, there is a maximum number alpha (G) of vertices that are mutually nonadjacent. A class of graphs, including the sum of an odd cycle C/sub 2n+3/(n>or=1) and a universal graph for which the Shannon capacity is not achieved by any finite power is described.>

The set of all the input probability distributions that achieve the capacity of a discrete memoryless channel (DMC) is obtained. A mathematical approach to characterize the simplicial subchannels inherent in the DMC is proposed to determine the desired set. A numerical example of an algorithm for calculating this set is also presented.