Abstract
This paper presents the construction and iterative decoding of low-density parity-check (LDPC) codes for channels affected by phase noise. The LDPC code is based on integer rings and designed to converge under phase-noisy channels. We assume that phase variations are small over short blocks of adjacent symbols. A part of the constructed code is inherently built with this knowledge and hence able to withstand a phase rotation of 2π/M radians, where M is the number of phase symmetries in the signal set, that occur at different observation intervals. Another part of the code estimates the phase ambiguity present in every observation interval. The code makes use of simple blind or turbo phase estimators to provide phase estimates over every observation interval. We propose an iterative decoding schedule to apply the sum-product algorithm (SPA) on the factor graph of the code for its convergence. To illustrate the new method, we present the performance results of an LDPC code constructed over Z4 with quadrature phase shift keying (QPSK) modulated signals transmitted over a static channel, but affected by phase noise, which is modeled by the Wiener (random-walk) process. The results show that the code can withstand phase noise of 2° standard deviation per symbol with small loss.
Highlights
In the past decade, plenty of work was done in the construction and decoding of low-density parity-check (LDPC) codes [1]
To illustrate the concepts discussed in this paper under a phasenoisy channel, we show the performance of an LDPC code constructed over Z4 with codewords mapped onto quadrature phase shift keying (QPSK) modulation, where the transmitted symbol sk ∈ {smk = e j((π/2)m+π/4)}, m = {0, 1, 2, 3}
We found that the code with sub-block size of 100 symbols gives the best bit-error rate (BER) performance for the amounts of phase noise considered in this paper
Summary
Plenty of work was done in the construction and decoding of LDPC codes [1]. In [6], the authors used smaller observation intervals to tackle varying frequency offset in the context of serially concatenated convolutional codes (SCCCs) They used blind and turbo phase estimators to provide a phase estimate for every sub-block. With a binary LDPC code, constructing global check nodes that converge irrespective of a phase rotation (a multiple of 2π/M radians) in the sub-blocks was difficult. We construct LDPC codes over rings with certain constraints on the placement of edges and edge gains such that they, along with sub-block phase estimation techniques, provide good performance under phase-noisy channels with low complexity. We present edge constraints based on integer rings generalized for any phase-symmetric modulation scheme, under which the convergence of the global check nodes is guaranteed in the presence of phase ambiguities in any sub-block.
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call