Interleaved concatenated coding for input-constrained channels

The foundation for the application of the recently introduced interleaved concatenated codes (parallel and serial) on digital data storage channels is steadily developing. This effort is being driven by the ever-increasing need for greater data storage densities as more and more of the data that is encountered in everyday use is transmitted and archived in digital format. The powerful error correction capabilities of these interleaved concatenated codes have been demonstrated by many researchers on channel models for both magnetic and optical storage—a lot more so for the former. These data storage channels are input-constrained, requiring that the binary sequences written to the channel obey certain constraints. Often, the soft-input requirements of the iterative decoders for the interleaved codes are difficult to meet with most constrained code decoders because a majority of these constraint decoders produce only binary decisions. The chief goal of this study is to directly address the interface between soft-input decoders for the error control code, and the output of the decoder for a constrained code. System configurations that allow the error control decoder access to reliable soft input in the presence of a constrained code are presented for both the memoryless additive white Gaussian noise (AWGN) channel and some precoded partial response (PR) channels. This is done within coded systems of both interleaved parallel and serial concatenated codes. We show how to implement these systems, provide simulation results, and analyze some of their properties. We also highlight the properties of some block constrained codes that affect the error rate performance of the overall system—in certain cases we show how these properties lead to the design of some good high-rate block constrained codes for use with iterative decoders. These block codes are matched to the channel (AWGN or precoded PR) in that the code properties are dictated by the constrained channel and its detector. We show that while the AWGN channel requires good Hamming distance properties from high-rate block constrained codes, precoded PR channels (ISI channels in general) detected with an a posteriori probability (APP) detector require codes containing significant a priori information about some of the code bits. In connection with the use of nonlinear block constrained codes, we show how to implement a soft-input, soft-output (SISO) decoder for a general nonlinear block code; we also compare the complexity of this computation to that for linear convolutional codes. Throughout the study, we focus on describing constrained-system configurations and the corresponding decoding techniques that allow a constrained code to be used with minimal accompanying rate loss. Some of these results are applicable to other digital communication systems that use both constrained codes and error-control codes. A constrained code is a good candidate for use in some systems with a data-derived timing signal. Systems that employ baseband line signaling with coding might be one such example.