Cyclic-Coded Integer-Forcing Equalization

A discrete-time intersymbol interference channel with additive Gaussian noise is considered, where only the receiver has knowledge of the channel impulse response. An approach for combining decision-feedback equalization with channel coding is proposed, where decoding precedes the removal of intersymbol interference. This is accomplished by combining the recently proposed integer-forcing equalization approach with cyclic block codes. The channel impulse response is linearly equalized to an integer-valued response. This is then utilized by leveraging the property that a cyclic code is closed under (cyclic) integer-valued convolution. Explicit bounds on the performance of the proposed scheme are also derived

Iterative Equalization and Source Decoding for Vector Quantized Sources

In this contribution an iterative (turbo) channel equalization and source decoding scheme is considered. In our investigations the source is modelled as a Gaussian-Markov source, which is compressed with the aid of vector quantization. The communications channel is modelled as a time-invariant channel contaminated by intersymbol interference (ISI). Since the ISI channel can be viewed as a rate-1 encoder and since the redundancy of the source cannot be perfectly removed by source encoding, a joint channel equalization and source decoding scheme may be employed for enhancing the achievable performance. In our study the channel equalization and the source decoding are operated iteratively on a bit-by-bit basis under the maximum aposteriori (MAP) criterion. The channel equalizer accepts the a priori information provided by the source decoding and also extracts extrinsic information, which in turn acts as a priori information for improving the source decoding performance. Simulation results are presented for characterizing the achievable performance of the iterative channel equalization and source decoding scheme. Our results show that iterative channel equalization and source decoding is capable of achieving an improved performance by efficiently exploiting the residual redundancy of the vector quantization assisted source coding

A Unified Framework for Linear-Programming Based Communication Receivers

It is shown that a large class of communication systems which admit a sum-product algorithm (SPA) based receiver also admit a corresponding linear-programming (LP) based receiver. The two receivers have a relationship defined by the local structure of the underlying graphical model, and are inhibited by the same phenomenon, which we call 'pseudoconfigurations'. This concept is a generalization of the concept of 'pseudocodewords' for linear codes. It is proved that the LP receiver has the 'maximum likelihood certificate' property, and that the receiver output is the lowest cost pseudoconfiguration. Equivalence of graph-cover pseudoconfigurations and linear-programming pseudoconfigurations is also proved. A concept of 'system pseudodistance' is defined which generalizes the existing concept of pseudodistance for binary and nonbinary linear codes. It is demonstrated how the LP design technique may be applied to the problem of joint equalization and decoding of coded transmissions over a frequency selective channel, and a simulation-based analysis of the error events of the resulting LP receiver is also provided. For this particular application, the proposed LP receiver is shown to be competitive with other receivers, and to be capable of outperforming turbo equalization in bit and frame error rate performance.Comment: 13 pages, 6 figures. To appear in the IEEE Transactions on Communication