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Register a new userOn the Typicality of the Linear Code Among the LDPC Coset Code Ensemble
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Added by
Chih-Chun Wang
Publication date
2005
fields
Informatics Engineering
and research's language is
English
Authors
Chih-Chun Wang
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Density evolution (DE) is one of the most powerful analytical tools for low-density parity-check (LDPC) codes on memoryless binary-input/symmetric-output channels. The case of non-symmetric channels is tackled either by the LDPC coset code ensemble (a channel symmetrizing argument) or by the generalized DE for linear codes on non-symmetric channels. Existing simulations show that the bit error rate performances of these two different approaches are nearly identical. This paper explains this phenomenon by proving that as the minimum check node degree $d_c$ becomes sufficiently large, the performance discrepancy of the linear and the coset LDPC codes is theoretically indistinguishable. This typicality of linear codes among the LDPC coset code ensemble provides insight into the concentration theorem of LDPC coset codes.
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Braided convolutional codes (BCCs) are a class of spatially coupled turbo-like codes that can be described by a $(2,3)$-regular compact graph. In this paper, we introduce a family of $(d_v,d_c)$-regular GLDPC codes with convolutional code constraints (CC-GLDPC codes), which form an extension of classical BCCs to arbitrary regular graphs. In order to characterize the performance in the waterfall and error floor regions, we perform an analysis of the density evolution thresholds as well as the finite-length ensemble weight enumerators and minimum distances of the ensembles. In particular, we consider various ensembles of overall rate $R=1/3$ and $R=1/2$ and study the trade-off between variable node degree and strength of the component codes. We also compare the results to corresponding classical LDPC codes with equal degrees and rates. It is observed that for the considered LDPC codes with variable node degree $d_v>2$, we can find a CC-GLDPC code with smaller $d_v$ that offers similar or better performance in terms of BP and MAP thresholds at the expense of a negligible loss in the minimum distance.
This work addresses the physical layer channel code design for an uncoordinated, frame- and slot-asynchronous random access protocol. Starting from the observation that collisions between two users yield very specific interference patterns, we define a surrogate channel model and propose different protograph low-density parity-check code designs. The proposed codes are both tested in a setup where the physical layer is abstracted, as well as on a more realistic channel model, where finite-length physical layer simulations of the entire asynchronous random access scheme, including decoding are carried out. We find that the abstracted physical layer model overestimates the performance when short blocks are considered. Additionally, the optimized codes show gains in supported channel traffic - a measure of the number of terminals that can be concurrently accommodated on the channel - of around 17% at a packet loss rate of 10^{-2} w.r.t. off-the-shelf codes.
This paper proposes a polar code construction scheme that reduces constituent-code supplemented decoding latency. Constituent codes are the sub-codewords with specific patterns. They are used to accelerate the successive cancellation decoding process of polar code without any performance degradation. We modify the traditional construction approach to yield increased number of desirable constituent codes that speeds the decoding process. For (n,k) polar code, instead of directly setting the k best and (n-k) worst bits to the information bits and frozen bits, respectively, we swap the locations of some information and frozen bits carefully according to the qualities of their equivalent channels. We conducted the simulation of 1024 and 2048 bits length polar codes with multiple rates and analyzed the decoding latency for various length codes. The numerical results show that the proposed construction scheme generally is able to achieve at least around 20% latency deduction with an negligible loss in gain with carefully selected optimization threshold.
The low-density parity-check (LDPC) lattices perform very well in high dimensions under generalized min-sum iterative decoding algorithm. In this work we focus on 1-level LDPC lattices. We show that these lattices are the same as lattices constructed based on Construction A and low-density lattice-code (LDLC) lattices. In spite of having slightly lower coding gain, 1-level regular LDPC lattices have remarkable performances. The lower complexity nature of the decoding algorithm for these type of lattices allows us to run it for higher dimensions easily. Our simulation results show that a 1-level LDPC lattice of size 10000 can work as close as 1.1 dB at normalized error probability (NEP) of $10^{-5}$.This can also be reported as 0.6 dB at symbol error rate (SER) of $10^{-5}$ with sum-product algorithm.
Projective Reed-Muller codes correspond to subcodes of the Reed-Muller code in which the polynomials being evaluated to yield codewords, are restricted to be homogeneous. The Generalized Hamming Weights (GHW) of a code ${cal C}$, identify for each dimension $ u$, the smallest size of the support of a subcode of ${cal C}$ of dimension $ u$. The GHW of a code are of interest in assessing the vulnerability of a code in a wiretap channel setting. It is also of use in bounding the state complexity of the trellis representation of the code. In prior work by the same authors, a code-shortening algorithm was employed to derive upper bounds on the GHW of binary projective, Reed-Muller (PRM) codes. In the present paper, we derive a matching lower bound by adapting the proof techniques used originally for Reed-Muller (RM) codes by Wei. This results in a characterization of the GHW hierarchy of binary PRM codes.
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