Some families of zero- error block codes for the two-user binary adder channel with feedback

Families of zero-error codes for the real binary adder channel with feedback that achieve high rate pairs are introduced. Two families of zero-error block codes are given for the case in which only one of the two senders receives feedback about the channel output. In the first of these families, the uninformed sender transmits at a rate of nearly one bit per symbol and the informed sender transmits slightly less that1/2bit per symbol. The second family is designed for the case in which the informed sender sends at or near one bit per symbol and the uninformed one sends nearly1/2bit per symbol. A family of zero-error codes is introduced, based on the Fibonacci recursion; these codes are readily implemented by means of a simple square-dividing strategy. The Fibonacci codes achieveR_{1}=R_{2}=log_{2} [(1 + sqrt{5})/2]in the limit of large block length. Time-sharing between members of these three code families is used to obtain an achievable rate region, or inner bound, to the zero-error capacity region for block coding. For the case in which the feedback is available to both senders, a variant of the Fibonacci difference equation is used to generate zero-error block codes with slightly higher asymptotic rateR_{1}=R_{2}=0.717.     

Some very simple codes for the nonsynchronized two-user multiple-access adder channel with binary inputs (Corresp.)

Some very simple codes are given for the two-user multiple-access adder channel with binary inputs that do not require word or bit synchronism between the encoders nor between the decoder and the encoders.     

A family of good uniquely decodable code pairs for the two-access binary adder channel

An explicit construction is presented of uniquely decodable code pairs for the two-access binary erasure channel. Through a computer search we found many code pairs coming from this construction with a rate pair above the nonconstructive lower bound known in the literature. Also presented is a simple uniquely decodable code pair, with a high rate pair, found by a different method.     

Nearly optimal multiuser codes for the binary adder channel

Coding schemes for the T-user binary adder channel are investigated. Recursive constructions are given for two families of mixed-rate, multiuser codes. It is shown that these basic codes can be combined by time-sharing to yield codes approaching most rates in the T-user capacity region. In particular, the best codes constructed herein achieve a sum-rate, R₁+...+R_T, which is higher than all previously reported codes for almost every T and is within 0.547-bit-per-channel use of the information-theoretic limit. Extensions to a T-user, Q-frequency adder channel are also discussed     

Code construction for the T-user noiseless adder channel

A general method for constructing codes for the T-user noiseless adder channel is proposed which achieves the largest sum rate known. The authors consider a multiple-access communication system. In this system, T statistically independent sources which use binary block codes C₁ ,...,C_T of equal length n, simultaneously transmit information via one common channel, maintaining synchronization with respect to words and bits. The output of the adder channel is the (T+l)-ary vector which is the component-wise arithmetic sum of the transmitted binary vectors. The task of the decoder is to uniquely determine the messages of all users     

Capacity bound for a noiseless T-user binary adder channel

The author proves an upper bound on the sum capacity of a noiseless T-user binary adder channel, thus settling a conjecture made by Chang and Weldon (1979). The bound is asymptotically tight and enables a more accurate performance evaluation of some very recent code constructions     

Good concatenated code ensembles for the binary erasure channel

In this work, we give good concatenated code ensembles for the binary erasure channel (BEC). In particular, we consider repeat multiple-accumulate (RMA) code ensembles formed by the serial concatenation of a repetition code with multiple accumulators, and the hybrid concatenated code (HCC) ensembles recently introduced by Koller et al. (5th Int. Symp. on Turbo Codes & Rel. Topics, Lausanne, Switzerland) consisting of an outer multiple parallel concatenated code serially concatenated with an inner accumulator. We introduce stopping sets for iterative constituent code oriented decoding using maximum a posteriori erasure correction in the constituent codes. We then analyze the asymptotic stopping set distribution for RMA and HCC ensembles and show that their stopping distance h_min, defined as the size of the smallest nonempty stopping set, asymptotically grows linearly with the block length. Thus, these code ensembles are good for the BEC. It is shown that for RMA code ensembles, contrary to the asymptotic minimum distance d_min, whose growth rate coefficient increases with the number of accumulate codes, the h_min growth rate coefficient diminishes with the number of accumulators. We also consider random puncturing of RMA code ensembles and show that for sufficiently high code rates, the asymptotic h_min does not grow linearly with the block length, contrary to the asymptotic d_min, whose growth rate coefficient approaches the Gilbert-Varshamov bound as the rate increases. Finally, we give iterative decoding thresholds for the different code ensembles to compare the convergence properties.     

Decoding of lineardelta-decodable codes for a multiple- access channel (Corresp.)

A scheme is presented for decoding lineardelta-decodable codes for the two-user noisy adder channel that exploits the linearity of the codes and corrects all patterns oflfloor (delta - 1)/2 rflooror fewer transmission errors.     

Error exponents for the two-user Poisson multiple-access channel

The error exponent of the two-user Poisson multiple-access channel under peak and average power constraints, but unlimited in bandwidth, is considered. First, a random coding lower bound on the error exponent is obtained, and an extension of Wyner's (1988) single-user codes is shown to be exponentially optimum for this case as well. Second, the sphere-packing bounding technique suggested by Burnashev and Kutoyants (see Probl. Inform. Transm., vol.35, no.2, p.3-22, 1999) is generalized to the case at hand and an upper bound on the error exponent, which coincides with the lower bound, is derived. Thus, this channel joins its single-user partner as one of very few for which the reliability function is known     

An upper bound for codes for the noisy two-access binary adder channel (Corresp.)

Using earlier methods a combinatorial upper bound is derived for|C|. cdot |D|, where(C,D)is adelta-decodable code pair for the noisy two-access binary adder channel. Asymptotically, this bound reduces toR_{1}=R_{2} leq frac{3}{2} + elog_{2} e - (frac{1}{2} + e) log_{2} (1 + 2e)= frac{1}{2} - e + H(frac{1}{2} - e) - frac{1}{2}H(2e),wheree = lfloor (delta - 1)/2 rfloor /n, n rightarrow inftyandR_{1}resp.R_{2}is the rate of the codeCresp.D.     

Limitations of the capacity of the M-user binary adder channel dueto physical considerations

The capacity of the M-user binary adder channel, subjected to various restrictions of physical nature, is investigated. The underlying propagation media considered are (i) fiber-optic, with lossless coupling and Poisson statistics, (ii) radio, under Rayleigh fading, and (iii) radio with constant amplitudes and random phases. Whereas the capacity of the unrestricted (ideal) model for the binary adder channel is known to increase without limit with the number of users, it is shown in the present paper that, for each of these cases, the total capacity is upper-bounded by a constant independent of the number of users: in case (i) by 1.7Q_T bits per channel use, where Q_T is the parameter of the Poisson process, in case (ii) by 4.33 bits per channel use, and in case (iii) by 4.27 bits per channel use     

Finite-length scaling of turbo-like code ensembles on the binary erasure channel

A possibility of estimating the finite-length performance of sparse-graph code ensembles gives two opportunities: to compare different codes of the same length in a context very close to real, practical applications and to perform the parameter optimization for a given code length [2]. We need a finite-length approximation that is valid for any code ensemble. The scaling approach seems to be a tool, general enough to provide such an approximation. However, the analytical derivation of parameters of the scaling approximation has been successful only for LDPC codes [1]; despite several attempts [25], [20], no such result was proposed for other code ensembles. In this paper, we focus on the finite-length performance of turbo-like codes, by applying the scaling approach to this case. In particular, by assuming the transmission over the binary erasure channel, we conjecture the scaling law and derive its scaling parameter. As examples, we present the performance estimation for Repeat-Accumulate codes [11], parallel turbo codes [8] and TLDPC codes [5], in all cases matching well the numerical results.     

An algorithm for calculating the exact bit error probability of a binary linear code over the binary symmetric channel

An efficient algorithm for calculating the ith bit error probability of a binary linear code over the binary symmetric channel (BSC) is presented. It is proved that the exact ith bit error probability of maximum-likelihood (ML) decoding, bounded distance decoding, and symbol-wise maximum a posteriori probability (MAP) decoding can be obtained with time complexity O(n2/sup n-k/), where n and k denote the length and the dimension of the target code. The proposed methods are applicable to any binary linear code with redundancy up to nearly 25-30 bits with a typical personal computer.     

Enhanced binary exponential backoff algorithm for fair channel access in the ieee 802.11 medium access control protocol

The medium access control protocol determines system throughput in wireless mobile ad hoc networks following the ieee 802.11 standard. Under this standard, asynchronous data transmissions have a defined distributed coordination function that allows stations to contend for channel usage in a distributed manner via the carrier sensing multiple access with collision avoidance protocol. In distributed coordination function, a slotted binary exponential backoff (BEB) algorithm resolves collisions of packets transmitted simultaneously by different stations. The BEB algorithm prevents packet collisions during simultaneous access by randomizing moments at stations attempting to access the wireless channels. However, this randomization does not eliminate packet collisions entirely, leading to reduced system throughput and increased packet delay and drop. In addition, the BEB algorithm results in unfair channel access among stations. In this paper, we propose an enhanced binary exponential backoff algorithm to improve channel access fairness by adjusting the manner of increasing or decreasing the contention window based on the number of the successfully sent frames. We propose several configurations and use the NS2 simulator to analyze network performance. The enhanced binary exponential backoff algorithm improves channel access fairness, significantly increases network throughput capacity, and reduces packet delay and drop. Copyright © 2013 John Wiley & Sons, Ltd.     

Uplink channel assignment with balanced load for code division multiple access cellular systems

In a code division multiple access (CDMA) wireless communication system, each mobile handset must be power controlled such that the power received at the base station is roughly the same. Otherwise, the interferences between mobile handsets will degrade the performance and increase the error rate. When a mobile handset uses channels from the neighbouring cells, it will raise its power to meet the threshold of signal strength. This will also increase the interference in the home cell. Therefore, we do not want a mobile handset to use channels from other cells blindly. In this paper, we propose an uplink channel assignment method based on the directed retry concept for CDMA cellular systems. The purpose is to achieve load balancing between neighbouring cells and at the same time controlling the interference levels at the base stations such that it will not affect the performance. Furthermore, priorities are given to handoff calls when assigning channels. Copyright © 2002 John Wiley & Sons, Ltd.     

Spreading code allocation strategy for downlink multicarrier code division multiple access transmission in a correlated Rayleigh fading channel

In this paper, we address the problem of multiple access interference (MAI) in a downlink multicarrier code division multiple access system. Because in the realistic case of correlated faded subcarriers, MAI greatly depends on the codes assigned to users, one way of improving performance without increasing receiver complexity consists in an appropriate code selection. We propose a code allocation strategy with the following properties: possible use with any code sequence and equalizer, low complexity, and efficient management of load variations. The allocation problem is formulated as a minimization problem of a cost function related to MAI. First, we provide analytical expressions for the channel frequency correlation function after maximum ratio combining, equal gain combining, and minimum mean square error equalization and for the MAI power. Then, by approximating these expressions, we define a simple cost function and build an iterative algorithm on the basis of the minimum maximum criterion to select the spreading codes. Finally, a complete analysis of the allocation efficiency is provided versus key parameters, in particular, the degree of correlation between the faded subcarriers, the system load, and the equalization techniques. Copyright © 2012 John Wiley & Sons, Ltd.     

Forward collision resolution-a technique for random multiple-accessto the adder channel

Consider M-Choose-T communications: T users or less, out of M potential users, are chosen at random to simultaneously transmit binary data over a common channel. A method for constructing codes that achieve error-free M-Choose-T communication over the noiseless adder channel (AC), at a nominal rate of 1/T bits per channel symbol per active user, is described and an efficient decoding procedure is presented. The use of such codes is referred to as forward collision resolution (FCR), as it enables correct decoding of collided messages without retransmissions. For any given T a code is available that yields a stable throughput arbitrarily close to 1 message/slot. Furthermore, if the occurrence of collisions is made known to the transmitters, such a throughput can be maintained for arbitrary T,T⩽M as well. If such feedback is not available, and T is random, the probability of an unresolved collision is significantly smaller than the probability of a collision in an uncoded system, at comparable message-arrival and information rates     

An improved achievable region for the discrete memoryless two-user multiple-access channel with noiseless feedback

An achievable region for the two-user discrete memoryless multiple-access channel (DMMAC) with noiseless feedback is proposed. The proposed region includes the Cover-Leung region, with the inclusion being, for some channels, strict. This inner bound is demonstrated for the ideal two-user Poisson multiple-access channel with noiseless feedback, in which case it is shown to improve on the Cover-Leung rate-sum.     

Packet multiple access for channel with binary feedback, capture, and multiple reception

This paper considers the multiple access of mobile users to a common wireless channel. The channel is slotted and the binary feedback (empty slot/nonempty slot) is sent to all accessing users. If a slot was not empty and only one user transmitted in it, the transmission is considered successful. Only the user, which had the successful transmission, receives information about its success. In the Introduction, the paper gives a review of known multiple-access algorithms for such a channel. Then our algorithm is constructed that has none of the weaknesses of the algorithms discussed in the Introduction. The algorithm is stable, in contrast to the ALOHA algorithm. It can work in a channel with capture and multiple reception. Without them, the algorithm has a throughput of 0.2891. It is shown how capture and multiple reception can increase the algorithm throughput to 0.6548 and decrease the packet delay for some fading models. The average packet delay and variance are found for two fading models. The models are Rayleigh fading with incoherent and coherent combining of joint interference power. The accessing traffic is Poisson.     

Game theoretic spectrum allocation for competing wireless access technologies to maximize the social welfare

Wireless Networks - Due to its scarce nature, the limited frequency spectrum must be effectively allocated to competing wireless access technologies. A promising approach is to consider frequency...