This paper creates a new cylindrical time-frequency network that can provide random multiple access by combining time division multiple access (TDMA) and frequency division multiple access (FDMA), abbreviated as TFDMA. A TFDMA-based transceiver is defined that uses a permutation matrix (PM) to model an n × n modulated matrix signal. The PM is isomorphic to a code word of an (n,n(n-1),n-1) permutation group code (PGC). An n-dimensional high-order multi-domain modulated signal constellation is thus created. The proposed TFDMA technique not only allows the maximum number of users to reach over 6000 in one second but also improves the anti-interference capacity for the existing compatible systems. In the same case of anti-interference capacity, should it become possible to overcome the one millisecond latency barrier, the maximum number of users could exceed 50000 in one second.
Cyclic redundancy check (CRC) codes combined with convolutional codes yield a powerful concatenated code that can be efficiently decoded using list decoding. To help design such systems, this paper presents an efficient algorithm for identifying the distance-spectrum-optimal (DSO) CRC polynomial for a given tail-biting convolutional code (TBCC) when the target undetected error rate (UER) is small. Lou et al. found that the DSO CRC design for a given zero-terminated convolutional code under low UER is equivalent to maximizing the undetected minimum distance (the minimum distance of the concatenated code). This paper applies the same principle to design the DSO CRC for a given TBCC under low target UER. Our algorithm is based on partitioning the tail-biting trellis into several disjoint sets of tail-biting paths that are closed under cyclic shifts. This paper shows that the tail-biting path in each set can be constructed by concatenating the irreducible error events (IEEs) and circularly shifting the resultant path. This motivates an efficient collection algorithm that aims at gathering IEEs, and a search algorithm that reconstructs the full list of error events with bounded distance of interest, which can be used to find the DSO CRC. Simulation results show that DSO CRCs can significantly outperform suboptimal CRCs in the low UER regime.
This paper proposes the low-complexity Chase (LCC) decoding using basis reduction (BR) interpolation for Reed-Solomon (RS) codes, namely the LCC-BR algorithm. With received soft information, a number of decoding test-vectors are formulated. The LCC-BR algorithm first constructs a common basis which will be utilized by the following individual basis constructions of all test-vectors. This eliminates the redundant computation in BR interpolation, resulting in a low decoding complexity. Moreover, the LCC-BR algorithm can decode each test-vector in parallel, lowering the decoding latency. This paper further proposes the progressive LCC-BR (PLCC-BR) algorithm that decodes the test-vectors sequentially and terminates once the intended message is found. This progressive decoding is realized without additional memory cost. Simulation results show the complexity and latency advantages of the proposed algorithms over the other benchmark algorithms.
In this paper, we propose a novel coding scheme, which is referred to as twisted-pair superposition transmission (TPST) and can be constructed from any given basic code by “mixing together” a pair of basic codewords in a “twisted” manner. We present a successive cancellation list decoding algorithm for TPST, where a list of candidates for the first layer is generated serially and the most competitive one is identified by combining the second layer. Thresholds on empirical divergence function (EDF) are introduced for early termination to trade off performance with decoding complexity. Genie-aided bounds are derived, indicating that the performance of TPST codes can be improved by employing partial superposition. Numerical simulation results show that, by taking tail-biting convolutional codes (TBCCs) as basic codes, we can construct TPST-TBCCs with near-capacity performance in the short length regime. The construction is flexible in the sense that it can be easily adapted to a wide range of coding rates.
This paper is motivated by polarization-multiplexed optical transmissions and the challenge of designing optimal modulation codes for the 2x2 MIMO fiber channel. This is a specific use case that diverges from the classical MIMO models as non-ergodicity and low-complexity are key. While rather simple from a fundamental viewpoint, the proposed optimal schemes appears to be geometrically pleasing as the second minimum distance turns out to be the object of interest and the associated vectors encode the basis of a regular tetrahedron in the affine space. More operationally, the newly developed polarization codes for single channel use achieve unit dB gains while keeping low implementation complexity.
We introduce Noise Recycling, a method that enhances decoding performance of channels subject to correlated noise without joint decoding. The method can be used with any combination of codes, code-rates and decoding techniques. In the approach, a continuous realization of noise is estimated from a lead channel by subtracting its decoded output from its received signal. This estimate is then used to improve the accuracy of decoding of an orthogonal channel that is experiencing correlated noise. In this design, channels aid each other only through the provision of noise estimates post-decoding. In a Gauss-Markov model of correlated noise, we constructively establish that noise recycling employing a simple successive order enables higher rates than not recycling noise. Simulations illustrate noise recycling can be employed with any code and decoder, and that noise recycling shows Block Error Rate (BLER) benefits when applying the same predetermined order as used to enhance the rate region. Finally, for short codes we establish that an additional BLER improvement is possible through noise recycling with racing, where the lead channel is not pre-determined, but is chosen on the fly based on which decoder completes first.