Ternary Feedback Research Articles

Computation of the efficiency of the Mosely-Humblet contention resolution algorithm: A simple method

Mosely and Humblet have obtained an efficient Contention Resolution Algorithm for transmission scheduling in a multi-user collision channel with ternary feedback (idle, success, collision). In this letter, a recursion for the expected value of the algorithm cycle delay is shown to reduce the computation of the efficiency and optimum partition functions to a simple optimization problem.

<tex>Q</tex>-ary collision resolution algorithms in random-access systems with free or blocked channel access

The throughput characteristics of contention-based random-access systems (RAS's) which use <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</tex> -ary tree algorithms (where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q \geq 2</tex> is the number of groups into which contending users are split) of the Capetanakis-Tsybakov-Mikhailov-Vvedenskaya type are analyzed for an infinite population of identical users generating packets according to a Poisson process. Both free and blocked channel-access protocols are considered in combination with <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</tex> -ary collision resolution algorithms that exploit either binary ("collision/no collision") or ternary ("collision/ success / idle") feedback. For the resulting RAS's, functional equations for transformed generating functions of the first two moments of the collision resolution interval length are obtained and solved. The maximum stable throughput as a function of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</tex> is given. The results of a packet-delay analysis are also given, and the analyzed RAS's are compared among themselves and with the slotted ALOHA system in terms of both system throughput and packet delay. It is concluded that the "practical optimum" RAS (in terms of ease of implementation combined with good performance) uses free (i.e., immediate) channel access and ternary splitting (i.e., <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q = 3</tex> ) with binary feedback.

Limited feedback sensing algorithms for the packet broadcast channel

A slotted packet broadcast channel with an infinite user population is considered. A limited feedback sensing algorithm is proposed and analyzed for collision versus noncollision binary feedback. The algorithm bas maximum throughput equal to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.42</tex> (packets/slot), has uniformly good delay characteristics within its stability region, and is robust in the presence of feedback errors. A variation of the algorithm, for ternary feedback, attains maximum throughput <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.425</tex> and bas uniformly good delay characteristics within its stability region. In contrast, the highest throughput limited feedback sensing algorithm existing for ternary feedback attains maximum throughput <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.456</tex> , but induces relatively high delays for Poisson intensities below <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.3</tex> .

On the throughput of degenerate intersection and first-come first-served collision resolution algorithms

It is shown that, for a ternary feedback random access channel with a Poisson arrival process, <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0.5</tex> is an upper bound to the throughput for all "degenerate intersection" algorithms (DIA's) and first-come first-served algorithms (FCFSA's). As a by-product, the nested FCFSA with the largest throughput is found for the random access channel with a Bernoulli arrival process with parameter <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</tex> . For <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p \geq 0.018</tex> , this algorithm has the highest throughput over all DIA's and FCFSA's. Lastly, it is shown that. for some values of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</tex> , a non-DIA, non-FCFSA has a higher throughput than the optimum DIA or FCFSA.

Ternary TTL chain code generator

This paper deals with the design and implementation of ternary shift register and ternary exclusive OR(TEx-OR) gates useful for ternary chain code realization. A linear TTL ternary feedback shift register (TFSR) is constructed and tested.

Nonlinear ternary feedback shift registers

A flexible theory of the general nonlinear ternary feedback shift register (fsr) is presented so that the inherent advantages of the ternary domain may be fully exploited in the fields of digital computers, communications, coding theory, and other areas where the device finds application. The authors show that the description afforded by the modulo-3 arithmetic functions may be adapted to provide a polynomial domain representation of these devices which is more flexible than other ternary operations. Methods of transforming the sequence domain behaviour of the device into this polynomial form, and vice-versa, are presented. Certain properties are isolated and the theory is extended by deriving the transforms required to produce certain related polynomial forms which correspond to simple operations in the sequence domain of the original fsr. The mechanism whereby two factor polynomials may be combined algebraically to produce a composite polynomial with exactly the same cycle set as a cascade connection of the two factors is fully investigated. Results concerning the related forms of these composite types are presented together with certain identities under the polynomial transforms.