We propose systematic fountain codes over GF (q) with the maximum likelihood (ML) decoding for distributed storage systems (DSS), which is called locality-improved repairable fountain codes (LIRFC). A generator matrix is constructed by entry-wise sampling and row-discarding, where the parameters are carefully determined such that locality is reduced while the ML decoding performance is not degraded. The degree distribution of the proposed codes is represented as a truncated and scaled binomial distribution with an optimized truncation threshold. Compared to the repairable fountain codes (RFC) that have logarithmic locality, the proposed codes achieve 5.97% to 22.44% less average locality than RFC, while having equivalent decoding failure probability and higher availability.

A generalization of unequal error protection (UEP) rateless codes and distributed rateless codes for distributed relay networks is proposed. We consider a two-hop relaying network where a single source transmits UEP rateless coded data to a destination via multiple relays. At the relays, the UEP rateless coded symbols are re-encoded by distributed rateless codes (DRC) to minimize the redundancy at the second hop. Previously introduced UEP rateless codes (URC) have supported a limited number of importance classes, mostly two classes, and targeted importance levels suited to a specific application. In this paper, however, we formulate an optimization problem to provide optimal URC in terms of the symbol error rate (SER) given any specific number and strengths of importance levels. Next, another optimization is proposed to obtain DRC with the minimum SER at a given overhead, which utilizes information of common symbols among the relays. The optimization methods are based on the AND-OR tree analysis and sequential quadratic programming. In addition, we evaluate the minimum achievable end-to-end symbol error rates over the wireless relay networks.

Several studies on fountain codes have proposed degree distribution optimization schemes to maximize symbol recovery rate. However, if the number of transmitted coded symbols is limited or the channel erasure probability is high, it may be impossible that a user recovers all of the data symbols regardless of degree distribution employed by the source. In this study, we focus on a new system model where one source transmits fountain-coded symbols to multiple users who already possess some data symbols and coded symbols. Assuming that each user can transmit a feedback packet containing its own state information before the source transmits coded symbols, we propose two types of degree distribution design schemes that are suitable for the system model. Simulation results demonstrate the efficiency of our proposed schemes by comparing with conventional methods in terms of symbol recovery rate and full recovery rate.

Rateless codes are representative capacity achieving codes for the binary erasure channels. We consider a network where multiple noncooperative sources with arbitrarily correlated messages communicate with a single destination. The conventional distributed rateless coding scheme introduces a general And-or tree analysis and provides linear programming (LP) based solutions only for some special cases. However, in this paper, an optimization method applicable to all the cases is proposed. Based on the generalized analysis, we define a new objective and employ the sequential quadratic programming (SQP) algorithm to solve the problem. The obtained solution contains optimal degree distributions and symbol-selection weights. It is shown that the proposed scheme exhibits the reduced overhead at the higher symbol recovery rate region compared to the conventional schemes.