Channel coding is a fundamental technology in wireless communication, which has attracted the efforts of many researchers around the world since its emergence. Fountain codes, with their exclusive features for long distances and a priori unknown channel state communication, provide a supreme approach with their famous rate-less property. The paper considers an evolution to distributed relay-based rate-less codes.

In the introductory discussion of the paper, a comprehensive, specific, and cohesive discussion concerned with rate-less/Luby transfer codes and distributed rate-less/Luby transfer codes is provided with references. Although a general multiple access relay network is the assumed environment, a new pattern called generalized distributed rate-less codes (GDRC) is proposed, and the concerned objectives and achievements are well demonstrated.

Two criteria, the probability distribution of the degree of the transmitted code symbols, which is a random variable between one and the number of information symbols, and the ripple size, which has been defined as the number of unprocessed symbols that haven’t recovered their neighbor in the decoding phase, have been considered for theoretical discussions. The authors, by defining lemmas and composing algorithms, try to dissect the influence of the variation of these parameters on the overall performance of the distributed relayed rate-less coding.

Discussions about unequal error protection when the average degree of each resource is different, overhead of distributed rate-less codes, optimization of degree distribution, utilizing the Jacobian matrix simplified to estimate the effect of small variation on each degree distribution, estimation of small change in ripple size, evolution of ripple size to approach the optimized ones, the quantity of encoded symbols to release all input symbols, and providing a comprehensive numerical result are the pivotal topics in the paper.

An analytical, well-structured analysis and comprehensive discussion concerned with the details of distributed relayed rate-less coding to gain performance in the defined platform are provided in the paper.