Multiple-access Collision Channel Research Articles

Multichannel Conflict-Avoiding Codes of Weights Three and Four

Conflict-avoiding codes (CACs) were introduced by Levenshtein as a single-channel transmission scheme for a multiple-access collision channel without feedback. When the number of simultaneously active source nodes is less than or equal to the weight of a CAC, it is able to provide a hard guarantee that each active source node transmits at least one packet successfully within a fixed time duration, no matter what the relative time offsets between the source nodes are. In this article, we extend CACs to multichannel CACs for providing such a hard guarantee over multiple orthogonal channels. Upper bounds on the number of codewords for multichannel CACs of weights three and four are derived, and constructions that are optimal with respect to these bounds are presented.

Classification of Strongly Conflict-Avoiding Codes

Strongly conflict-avoiding codes (SCACs) for slot-asynchronous multiple-access collision channels without feedback are considered. Codes with maximum size (optimal codes) for given parameters are of interest. In this letter, we present classification results about optimal SCACs of weights 3, 4, and 5 and given small lengths. We also determine some previously unknown values of the size of optimal SCACs with these parameters.

Classification of optimal conflict-avoiding codes of weights 6 and 7

A conflict-avoiding code is used to guarantee that each transmitting user can send at least one packet successfully within a fixed period of time, provided that at most k out of M potential users are active simultaneously in a multiple-access collision channel. The number of codewords in a conflict-avoiding code determines the number M of potential users that can be supported in a system. That is why codes of the maximum cardinality for given parameters (optimal codes) are of interest. In this paper we determine the values of the maximum cardinality and classify up to multiplier equivalence optimal conflict-avoiding codes for 6 and 7 active users and given small lengths.

Optimal conflict-avoiding codes for 3, 4 and 5 active users

Conflict-avoiding codes are used in multiple-access collision channels without feedback. The number of codewords in a conflict-avoiding code is the number of potential users of the channel. That is why codes with maximum cardinality (optimal codes) for given parameters are of interest. In this paper we classify, up to multiplier equivalence, all optimal conflict-avoiding codes of weights 3, 4, and 5 and given small lengths. We also determine some previously unknown values of the maximum cardinality of conflict-avoiding codes of weights 4 and 5.

Strongly Conflict-Avoiding Codes with Weight Three

Strongly conflict-avoiding codes are used in the asynchronous multiple-access collision channel without feedback. The number of codewords in a strongly conflict-avoiding code is the number of potential users that can be supported in the system. In this paper, an improved upper bound on the size of strongly conflict-avoiding codes of length $$n$$n and weight three is obtained. This bound is further shown to be tight for some cases by direct constructions.

Optimal strongly conflict-avoiding codes of even length and weight three

Strongly conflict-avoiding codes (SCACs) are employed in a slot-asynchronous multiple-access collision channel without feedback to guarantee that each active user can send at least one packet successfully in the worst case within a fixed period of time. Assume all users are assigned distinct codewords, the number of codewords in an SCAC is equal to the number of potential users that can be supported. SCACs have different combinatorial structure compared with conflict-avoiding codes (CACs) due to additional collisions incurred by partially overlapped transmissions. In this paper, we establish upper bounds on the size of SCACs of even length and weight three. Furthermore, it is shown that some optimal CACs can be used to construct optimal SCACs of weight three.

Binary Sequences for Multiple Access Collision Channel: Identification and Synchronization

In this paper we investigate the identification and synchronization problems on a multiple access collision channel. Following Massey's lead, solutions to these problems are addressed by protocol sequences. This paper considers two different levels of user synchroneity: frame-synchronous access and slot-synchronous access. For the identification problem, we study user-detectable sequences. These are sequences with the cross-correlation property that allows each active user be detected within a bounded delay basing only on the channel activity information observed. Furthermore, we investigate the synchronization problem for delay-detectable sequences under the slot-synchronous access assumption. The goal of the synchronization problem is to determine the offset relations among all the active users. Sequences that allow such determination can be viewed as a special subset of user-detectable sequences. For both of these sequence families, it is desirable that the sequence length should be as short as possible. Hence, it is important to derive the minimum sequence lengths for these respective families. This is an extremely difficult open problem. Nevertheless, lower and upper bounds on these minimum lengths are presented in this paper under different levels of synchroneity assumptions. In addition, the performance of these sequences is demonstrated via numerical simulation.

New optimal constructions of conflict-avoiding codes of odd length and weight 3

Conflict-avoiding codes (CACs) have played an important role in multiple-access collision channel without feedback. The size of a CAC is the number of codewords which equals the number of potential users that can be supported in the system. A CAC with maximal code size is said to be optimal. The use of an optimal CAC enables the largest possible number of asynchronous users to transmit information efficiently and reliably. In this paper, the maximal sizes of both equidifference and non equidifference CACs of odd prime length and weight 3 are obtained. Meanwhile, the optimal constructions of both equidifference and non equidifference CACs are presented. The numbers of equidifference and non equidifference codewords in an optimal code are also obtained. Furthermore, a new modified recursive construction of CACs for any odd length is shown. Non equidifference codes can be constructed in this method.

Strongly Conflict-Avoiding Codes

Strongly conflict-avoiding codes (SCACs) are used in the slot-asynchronous multiple-access collision channel without feedback to guarantee that each active user can send at least one packet successfully in the worst case within a fixed period of time. The number of codewords in an SCAC is the number of potential users that can be supported. In this paper, a general upper bound on the size of SCAC is derived. We further improve the upper bound if the code has some special structure, called equi-difference, and we show this bound is asymptotically tight.

A General Upper Bound on the Size of Constant-Weight Conflict-Avoiding Codes

Conflict-avoiding codes are used in the multiple-access collision channel without feedback. The number of codewords in a conflict-avoiding code is the number of potential users that can be supported in the system. In this paper, a new upper bound on the size of conflict-avoiding codes is proved. This upper bound is general in the sense that it is applicable to all code lengths and all Hamming weights. Several existing constructions for conflict-avoiding codes, which are known to be optimal for Hamming weights equal to four and five, are shown to be optimal for all Hamming weights in general.

Analysis of Collision Channel with Asynchronous Access

A T user multiple access collision channel without feedback is considered where the channel inputs are called packets. The packets take values from non-binary input alphabet. It is supposed that at most M users are active, i.e., are communicating simultaneously (2 ≤ M <<T). We are looking for codes and protocol sequences of users of minimum length such that from the output of the channel it can be determined which users were active, what were their synchron positions, and what they sent.

Modulation and coding for the Gaussian collision channel

We study signal-space coding for coherent slow frequency-hopped communications over a Gaussian multiple-access collision channel (G-MACC). We define signal sets and interleavers having maximum collision resistance. The packet-error probability and the spectral efficiency obtained by these signal sets concatenated with outer block coding and hard (error-only) decoding is evaluated without assuming perfect interleaving. Closed-form expressions are provided and computer simulations show perfect agreement with analysis. The structure of good interleavers is also discussed. More generally, we present expressions for the information outage probability and for the achievable (ergodic) rate of the G-MACC at hand, under various assumptions on user coding and decoding strategies. The outage probability yields the limiting packet-error probability with finite interleaving depth (delay-limited systems). The achievable rate yields the limiting system spectral efficiency for large interleaving depth (delay-unconstrained systems). Comparisons with other classical multiple-access schemes are provided.

Constructions of protocol sequences for multiple access collision channel without feedback

Constructions of protocol sequences for multiple-access collision channel without feedback are given. These constructions are the extensions of those described by A, Gyorfi, and Massey (see ibid., vol.38, p. 940, May 1992). If the basic code in their constructions, a Reed-Solomon code, is replaced by a BCH code then the resulting protocol sequences have the feature that, for a given sum rate, the ratio of the total user population to the block length becomes much larger. >

Near-optimum control of multiple-access collision channels

A method based on recursive computation of the expected number of attempts and successes during the collision resolution phase of an access control algorithm is introduced for the design of near-optimum control strategies for multiple access collision channels with ternary and binary feedback. With this approach it is possible to circumvent the extremely difficult and still unsolved problem of finding the access control algorithm which achieves the highest throughput by settling for a near-optimum solution. The key to the design of the algorithms is to approximate the originally infinite-dimensional optimization problem by a one-dimensional optimization problem. In the ternary feedback case, the proposed algorithm achieves a throughput virtually identical to the highest throughput reported. Several forms of binary feedback are considered, and algorithms are introduced that achieve the highest throughput reported. >