6,922 research outputs found
Partitioned List Decoding of Polar Codes: Analysis and Improvement of Finite Length Performance
Polar codes represent one of the major recent breakthroughs in coding theory
and, because of their attractive features, they have been selected for the
incoming 5G standard. As such, a lot of attention has been devoted to the
development of decoding algorithms with good error performance and efficient
hardware implementation. One of the leading candidates in this regard is
represented by successive-cancellation list (SCL) decoding. However, its
hardware implementation requires a large amount of memory. Recently, a
partitioned SCL (PSCL) decoder has been proposed to significantly reduce the
memory consumption. In this paper, we examine the paradigm of PSCL decoding
from both theoretical and practical standpoints: (i) by changing the
construction of the code, we are able to improve the performance at no
additional computational, latency or memory cost, (ii) we present an optimal
scheme to allocate cyclic redundancy checks (CRCs), and (iii) we provide an
upper bound on the list size that allows MAP performance.Comment: 2017 IEEE Global Communications Conference (GLOBECOM
Construction of Capacity-Achieving Lattice Codes: Polar Lattices
In this paper, we propose a new class of lattices constructed from polar
codes, namely polar lattices, to achieve the capacity \frac{1}{2}\log(1+\SNR)
of the additive white Gaussian-noise (AWGN) channel. Our construction follows
the multilevel approach of Forney \textit{et al.}, where we construct a
capacity-achieving polar code on each level. The component polar codes are
shown to be naturally nested, thereby fulfilling the requirement of the
multilevel lattice construction. We prove that polar lattices are
\emph{AWGN-good}. Furthermore, using the technique of source polarization, we
propose discrete Gaussian shaping over the polar lattice to satisfy the power
constraint. Both the construction and shaping are explicit, and the overall
complexity of encoding and decoding is for any fixed target error
probability.Comment: full version of the paper to appear in IEEE Trans. Communication
From Polar to Reed-Muller Codes: a Technique to Improve the Finite-Length Performance
We explore the relationship between polar and RM codes and we describe a
coding scheme which improves upon the performance of the standard polar code at
practical block lengths. Our starting point is the experimental observation
that RM codes have a smaller error probability than polar codes under MAP
decoding. This motivates us to introduce a family of codes that "interpolates"
between RM and polar codes, call this family , where is
the original polar code, and is an RM code.
Based on numerical observations, we remark that the error probability under MAP
decoding is an increasing function of . MAP decoding has in general
exponential complexity, but empirically the performance of polar codes at
finite block lengths is boosted by moving along the family even under low-complexity decoding schemes such as, for instance,
belief propagation or successive cancellation list decoder. We demonstrate the
performance gain via numerical simulations for transmission over the erasure
channel as well as the Gaussian channel.Comment: 8 pages, 7 figures, in IEEE Transactions on Communications, 2014 and
in ISIT'1
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