This paper presents generalized expressions for the probabilities of correct decoding and decoder error for Reed-Solomon (RS) codes. In these expressions, the symbol error and erasure probabilities are different in each coordinate in a codeword. The above expressions are used to derive the expressions for reliability and delay for Type-I hybrid ARQ (HARQ-I) systems when each symbol in a packet (multiple codewords per packet) has unique symbol error and erasure probabilities. Applications of the above results are demonstrated by analyzing a bursty-correlative channel in which the symbols and codewords within the packet are correlated.

This paper presents a new analytic framework for determining the reliability and average delay for a satellite communication system that uses a modified hybrid ARQ protocol for retransmission procedure. Key to the analysis is a method for explicitly determining decoder error and failure probabilities for a channel characterized by multiple dependent symbol error and erasure probabilities. In addition, a new method for determining the delay and reliability for a hybrid ARQ protocol using selective retransmission of codewords is derived for a system that utilizes multiple codewords per packet. The two techniques provide the capabilities of investigating different wireless multimedia satellite networks with variety of retransmission protocols and access methods.

The performance of frequency-hop spread-spectrum (FHSS) communication systems using hybrid automatic-repeat-request (ARQ) can be improved by combining current and prior transmissions at the receiver. Two methods for combining packets in systems that employ interleaving and Reed-Solomon (RS) coding are presented and analyzed for the partial-band interference channel. These methods use majority logic combining at the codeword level to make retransmission decisions. Bounded distance errors-and-erasures decoding and erasure generation by means of Viterbi's ratio threshold test (RTT) are incorporated in the analysis. Results of the analysis show that, with comparable packet error probabilities, the packet-combining schemes provide significant gains in throughput when compared with systems that do not employ combining.

In this letter, formulas for the total number of decodable and undecodable vectors are derived for a general (n,k) q-ary linear block code. These formulas are used to find the probabilities of decoder error and decoder failure for Reed-Solomon codes under errors-and-erasures decoding. The resulting analytical expressions are computationally efficient and allow accurate calculation of very small values of decoder failure probabilities. The formulas are used to analyze the performance of type-I hybrid automatic-repeat-request (HARQ) protocols with two decoding diameters.

We present a framework for determining the exact decoder error and failure probabilities for linear block codes in a frequency-hop communication channel with an arbitrary number of conditional symbol error and erasure probabilities. Applications are demonstrated for type-I hybrid ARQ systems by deriving equations for the packet error probability and throughput. Because these quantities are too small to be obtained by simulation, the framework provides exact results which are unobtainable by previous work.