Algorithms for decoding block codes.

Abstract

Practical decoding algorithms for channels with unknown (or varying) statistics are highly desired in real applications. In this thesis two decoders are proposed and analyzed in different environments. The first decoder proposed is for a powerful class of codes known as concatenated codes which consist of an inner code and an outer code. The decoder consists of a number of decoders operating in parallel and a decision device that selects one of their outputs. Each of the parallel decoders consists of a soft decision inner decoder which processes the received vector and outputs either an estimate or an erasure to an outer decoder. Each of the inner decoders has a different threshold for deciding when to erase and the corresponding outer decoder is matched to it. The decision devise then chooses the codeword that is closest to the received vector, as the transmitted codeword. This form of parallel decoding is useful for channels with unknown interference, because the parallel decoders can be matched to different channels and the decision device can choose, for a given channel, the most likely transmitted codeword. We find the "optimum" threshold settings to maximize the error-correcting capability of the code by analyzing a game with the channel and decoder as opponents. The second decoder is for a coded frequency hopped spread spectrum communication system subject to Rayleigh fading. The decoder makes use of some noisy side information related to the reliability of the symbols in a transmitted hop. This side information is generated at the receiver by forming a statistic using the outputs of the demodulator, upon which we decide whether a received symbol is reliable or not. If a symbol is declared unreliable, we erase that symbol and present it to the decoder. The performance of such a system is evaluated for repetition coding, Reed-Solomon codes, and concatenated codes. We show that for a channel with fading the use of this side information can lead to a significant enhancement in the performance of a slow-frequency-hop communication system that employs coding.