Reliability information in channel decoding : practical aspects and information theoretical bounds
This thesis addresses the use of reliability information in channel decoding. The considered transmission systems comprise linear binary channel encoders, symmetric memoryless communication channels, and non-iterative or iterative symbol-by-symbol soft-output channel decoders. The notions of accurate and mismatched reliability values are introduced, and the measurement and improvement of the quality of reliability values are discussed. A criterion based on the Kullback-Leibler distance is proposed to assess the difference between accurate and mismatched reliability values. Accurate reliability values may be exploited to estimate transmission quality parameters, such as the bit-error probability or the symbol-wise mutual information between encoder input and decoder output. The proposed method is unbiased, does not require knowledge of the transmitted data, and has a smaller estimation variance than the conventional method. Symbol-by-symbol soft-output decoding may be interpreted as processing of mutual information. The behavior of a decoder may be characterized by information transfer functions, such as information processing characteristics (IPCs) or extrinsic information transfer (EXIT) functions. Bounds on information transfer functions are derived using the concept of bounding combined information. The resulting bounds are valid for all binary-input symmetric memoryless channels. Single parity-check codes, repetition codes, and the accumulator are addressed. Based on such bounds, decoding thresholds for low-density parity-check codes are analytically determined.