MUCHO: Two problems in Multi User Coding for High Occupancy Channels

Catholic University Of America, Washington DC

Investigators

Abstract

Intellectual Merit Attaining broadcast channel capacity relies on dirty paper coding using nested lattice codes and quantization to codewords from a given coset; this in turn can be reduced to nearest-neighbor or maximum likelihood decoding, solved in principle by the Viterbi algorithm applied to trellis codes. Capacity-approaching codes, however, have trellis descriptions with prohibitive complexities, restricting this technique to (lower performance)convolutional codes. Code word quantization via iterative decoding, which has links to constrained maximum likelihood sequence estimation, regrettably fails here as well, as documented within. To overcome these limitations, we investigate successive code word quantization in two forms: the first draws on the rich structure of reduced-order Hankel-norm approximation from system theory, and pursues its adaptation to trellis descriptions of capacity-approaching codes over finite fields. The goal is to obtain a reduced order (hence, lower complexity) trellis description amenable to Viterbi decoding, which in turn serves as the initial point for finer code word quantization. A parallel approach studies quantization decoding" using the variable code rate structure innate to nested codes; quantization is first performed using a higher rate code, which rate is progressively reduced to the target rate. The second problem concerns code book generation for multiple access channels. This draws on pseudorandom interleaver design using modular arithmetic over prime factor fields, in order to parametrically generate distinct user codes with minimal overlap. Unlike direct-sequence CDMA, whose spreading sequences are repetition codes devoid of coding gain, users are distinguished by their channel codes without additional rate loss from spreading sequences. The proposed technique generalizes the recently introduced interleaver division multiple access (IDMA) scheme, and preliminary results indicate improved performance in specific scenarios. In addition, by recasting interleavers as decryption keys, relations to secrecy systems will likewise be developed. The proposed framework accommodates secrecy suitable for mobile wireless systems, offering negligible overhead and freedom from export restrictions that may accompany strong encryption, as a first-line defense that must accompany the ubiquity of wireless network expanstion. Broader Impact In addition to the direct benefits to multi-user communications from the expected results, many of the coding/decoding configurations to be studied in the proposed research will be integrated into senior and graduate level courses taught at the Catholic University of America, in the form of design projects that enhance students' abilities to master the interaction between information theory and reliable communications. In addition, Hankel norm approximation tools, which have traditionally been better developed in the control field, may serve to bridge some traditional divides between systems and communications researchers.