A Randomized Construction of Polar Subcodes

A method for construction of polar subcodes is presented, which aims on minimization of the number of low-weight codewords in the obtained codes, as well as on improved performance under list or sequential decoding. Simulation results are provided, which show that the obtained codes outperform LDPC and turbo codes.Comment: Accepted to ISIT 2017 Formatting change

Decoding Strategies at the Relay with Physical-Layer Network Coding

Cataloged from PDF version of article.A two-way relay channel is considered where two users exchange information via a common relay in two transmission phases using physical-layer network coding (PNC). We consider an optimal decoding strategy at the relay to decode the network coded sequence during the first transmission phase, which is approximately implemented using a list decoding (LD) algorithm. The algorithm jointly decodes the codewords transmitted by the two users and sorts the L most likely pair of sequences in the order of decreasing a-posteriori probabilities, based on which, estimates of the most likely network coded sequences and the decoding results are obtained. Using several examples, it is observed that a lower complexity alternative, that jointly decodes the two transmitted codewords, has a performance similar to the LD based decoding and offers a near-optimal performance in terms of the error rates corresponding to the XOR of the two decoded sequences. To analyze the error rate at the relay, an analytical approximation of the word-error rate using the joint decoding (JD) scheme is evaluated over an AWGN channel using an approach that remains valid for the general case of two users adopting different codebooks and using different power levels. We further extend our study to frequency selective channels where two decoding approaches at the relay are investigated, namely; a trellis based joint channel detector/physical-layer network coded sequence decoder (JCD/PNCD) which is shown to offer a near-optimal performance, and a reduced complexity channel detection based on a linear receiver with minimum mean squared error (MMSE) criterion which is particularly useful where the number of channel taps is large

The Road From Classical to Quantum Codes: A Hashing Bound Approaching Design Procedure

Powerful Quantum Error Correction Codes (QECCs) are required for stabilizing and protecting fragile qubits against the undesirable effects of quantum decoherence. Similar to classical codes, hashing bound approaching QECCs may be designed by exploiting a concatenated code structure, which invokes iterative decoding. Therefore, in this paper we provide an extensive step-by-step tutorial for designing EXtrinsic Information Transfer (EXIT) chart aided concatenated quantum codes based on the underlying quantum-to-classical isomorphism. These design lessons are then exemplified in the context of our proposed Quantum Irregular Convolutional Code (QIRCC), which constitutes the outer component of a concatenated quantum code. The proposed QIRCC can be dynamically adapted to match any given inner code using EXIT charts, hence achieving a performance close to the hashing bound. It is demonstrated that our QIRCC-based optimized design is capable of operating within 0.4 dB of the noise limit

An Iterative Receiver for OFDM With Sparsity-Based Parametric Channel Estimation

In this work we design a receiver that iteratively passes soft information between the channel estimation and data decoding stages. The receiver incorporates sparsity-based parametric channel estimation. State-of-the-art sparsity-based iterative receivers simplify the channel estimation problem by restricting the multipath delays to a grid. Our receiver does not impose such a restriction. As a result it does not suffer from the leakage effect, which destroys sparsity. Communication at near capacity rates in high SNR requires a large modulation order. Due to the close proximity of modulation symbols in such systems, the grid-based approximation is of insufficient accuracy. We show numerically that a state-of-the-art iterative receiver with grid-based sparse channel estimation exhibits a bit-error-rate floor in the high SNR regime. On the contrary, our receiver performs very close to the perfect channel state information bound for all SNR values. We also demonstrate both theoretically and numerically that parametric channel estimation works well in dense channels, i.e., when the number of multipath components is large and each individual component cannot be resolved.Comment: Major revision, accepted for IEEE Transactions on Signal Processin

Novel Methods in the Improvement of Turbo Codes and their Decoding

The performance of turbo codes can often be improved by improving the weight spectra of such codes. Methods of producing the weight spectra of turbo codes have been investigated and many improvements were made to refine the techniques. A much faster method of weight spectrum evaluation has been developed that allows calculation of weight spectra within a few minutes on a typical desktop PC. Simulation results show that new high performance turbo codes are produced by the optimisation methods presented. The two further important areas of concern are the code itself and the decoding. Improvements of the code are accomplished through optimisation of the interleaver and choice of constituent coders. Optimisation of interleaves can also be accomplished automatically using the algorithms described in this work. The addition of a CRC as an outer code proved to offer a vast improvement on the overall code performance. This was achieved without any code rate loss as the turbo code is punctured to make way for the CRC remainder. The results show a gain of 0.4dB compared to the non-CRC (1014,676) turbo code. Another improvement to the decoding performance was achieved through a combination of MAP decoding and Ordered Reliability decoding. The simulations show a performance of just 0.2dB from the Shannon limit. The same code without ordered reliability decoding has a performance curve which is 0.6dB from the Shannon limit. In situations where the MAP decoder fails to converge ordered reliability decoding succeeds in producing a codeword much closer to the received vector, often the correct codeword. The ordered reliability decoding adds to the computational complexity but lends itself to FPGA implementation.Engineering and Physical Sciences Research Council (EPSRC