Construction and Applications of CRT Sequences

Protocol sequences are used for channel access in the collision channel without feedback. Each user accesses the channel according to a deterministic zero-one pattern, called the protocol sequence. In order to minimize fluctuation of throughput due to delay offsets, we want to construct protocol sequences whose pairwise Hamming cross-correlation is as close to a constant as possible. In this paper, we present a construction of protocol sequences which is based on the bijective mapping between one-dimensional sequence and two-dimensional array by the Chinese Remainder Theorem (CRT). In the application to the collision channel without feedback, a worst-case lower bound on system throughput is derived.Comment: 16 pages, 5 figures. Some typos in Section V are correcte

Multiple accessing for the collision channel without feedback

Bibliography: p. 582."September 1984." Reprinted from IEEE Journal on Selected Areas in Communications, vol. SAC-2, no.4, July 1984."...National Science Foundation... Grant NSF/ECS-79-19880." "...Advanced Research Project Agency... Grant ONR/N00014-75-C1183."Joseph Y.N. Hui

Coded Slotted ALOHA: A Graph-Based Method for Uncoordinated Multiple Access

In this paper, a random access scheme is introduced which relies on the combination of packet erasure correcting codes and successive interference cancellation (SIC). The scheme is named coded slotted ALOHA. A bipartite graph representation of the SIC process, resembling iterative decoding of generalized low-density parity-check codes over the erasure channel, is exploited to optimize the selection probabilities of the component erasure correcting codes via density evolution analysis. The capacity (in packets per slot) of the scheme is then analyzed in the context of the collision channel without feedback. Moreover, a capacity bound is developed and component code distributions tightly approaching the bound are derived.Comment: The final version to appear in IEEE Trans. Inf. Theory. 18 pages, 10 figure

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.Comment: 10 pages, 1 figur

Constant Delivery Delay Protocol Sequences for the Collision Channel Without Feedback

International audienceWe consider a collision channel model without feedback based on a time-slotted communication channel shared by K users. In this model, packets transmitted in the same time slot collide with each other and are unrecoverable. Each user accesses the channel according to an internal periodical pattern called protocol sequence. Due to the lack of feedback, users cannot synchronize their protocol sequences, leading to unavoidable collisions and varying throughput. Protocol sequences that provide constant throughput regardless of delay offsets between users are called shift-invariant (SI), they have been studied and characterized in previous work. We propose a new class of SI sequences: Constant Individual Delivery Delay (CIDD) sequences which ensure that the delay between two successfully delivered packets is constant for each user. We present a characterization of CIDD sequences. We also prove that CIDD sequences can achieve the lower bound of SI sequences period but not the optimal throughput