142 research outputs found
Enhanced Recursive Reed-Muller Erasure Decoding
Recent work have shown that Reed-Muller (RM) codes achieve the erasure
channel capacity. However, this performance is obtained with maximum-likelihood
decoding which can be costly for practical applications. In this paper, we
propose an encoding/decoding scheme for Reed-Muller codes on the packet erasure
channel based on Plotkin construction. We present several improvements over the
generic decoding. They allow, for a light cost, to compete with
maximum-likelihood decoding performance, especially on high-rate codes, while
significantly outperforming it in terms of speed
Magic state distillation with punctured polar codes
We present a scheme for magic state distillation using punctured polar codes.
Our results build on some recent work by Bardet et al. (ISIT, 2016) who
discovered that polar codes can be described algebraically as decreasing
monomial codes. Using this powerful framework, we construct tri-orthogonal
quantum codes (Bravyi et al., PRA, 2012) that can be used to distill magic
states for the gate. An advantage of these codes is that they permit the
use of the successive cancellation decoder whose time complexity scales as
. We supplement this with numerical simulations for the erasure
channel and dephasing channel. We obtain estimates for the dimensions and error
rates for the resulting codes for block sizes up to for the erasure
channel and for the dephasing channel. The dimension of the
triply-even codes we obtain is shown to scale like for the binary
erasure channel at noise rate and for the dephasing
channel at noise rate . The corresponding bit error rates drop to
roughly for the erasure channel and for
the dephasing channel respectively.Comment: 18 pages, 4 figure
Improved Successive Cancellation Decoding of Polar Codes
As improved versions of successive cancellation (SC) decoding algorithm,
successive cancellation list (SCL) decoding and successive cancellation stack
(SCS) decoding are used to improve the finite-length performance of polar
codes. Unified descriptions of SC, SCL and SCS decoding algorithms are given as
path searching procedures on the code tree of polar codes. Combining the ideas
of SCL and SCS, a new decoding algorithm named successive cancellation hybrid
(SCH) is proposed, which can achieve a better trade-off between computational
complexity and space complexity. Further, to reduce the complexity, a pruning
technique is proposed to avoid unnecessary path searching operations.
Performance and complexity analysis based on simulations show that, with proper
configurations, all the three improved successive cancellation (ISC) decoding
algorithms can have a performance very close to that of maximum-likelihood (ML)
decoding with acceptable complexity. Moreover, with the help of the proposed
pruning technique, the complexities of ISC decoders can be very close to that
of SC decoder in the moderate and high signal-to-noise ratio (SNR) regime.Comment: This paper is modified and submitted to IEEE Transactions on
Communication
Successive Cancellation Ordered Search Decoding of Modified -Coset Codes
A tree search algorithm called successive cancellation ordered search (SCOS)
is proposed for -coset codes that implements
maximum-likelihood (ML) decoding with an adaptive complexity for transmission
over binary-input AWGN channels. Unlike bit-flip decoders, no outer code is
needed to terminate decoding; therefore, SCOS also applies to
-coset codes modified with dynamic frozen bits. The average
complexity is close to that of successive cancellation (SC) decoding at
practical frame error rates (FERs) for codes with wide ranges of rate and
lengths up to bits, which perform within dB or less from the
random coding union bound and outperform Reed--Muller codes under ML decoding
by up to dB. Simulations illustrate simultaneous gains for SCOS over
SC-Fano, SC stack (SCS) and SC list (SCL) decoding in FER and the average
complexity at various SNR regimes. SCOS is further extended by forcing it to
look for candidates satisfying a threshold on the likelihood, thereby
outperforming basic SCOS under complexity constraints. The modified SCOS
enables strong error-detection capability without the need for an outer code.
In particular, the PAC code under modified SCOS provides gains in
overall and undetected FER compared to CRC-aided polar codes under SCL/dynamic
SC flip decoding at high SNR.Comment: 14 pages, 9 figures, 3 tables. Submitted to IEEE journal. The revised
version of the first submission. Major changes: 1) No dedicated section for
numerical results. Instead, simulations are provided right after the relevant
section. 2) More simulation results are added to compare all the state of art
polar decoders in terms of the number of arithmetic operations. arXiv admin
note: text overlap with arXiv:2105.0404
Two-Layer Coded Channel Access With Collision Resolution: Design and Analysis
We propose a two-layer coding architecture for communication of multiple users over a shared slotted medium enabling joint collision resolution and decoding. Each user first encodes its information bits with an outer code for reliability, and then transmits these coded bits with possible repetitions over transmission time slots of the access channel. The transmission patterns are dictated by the inner collision-resolution code and collisions with other users’ transmissions may occur. We analyze two types of codes for the outer layer: long-blocklength LDPC codes, and short-blocklength algebraic codes. With LDPC codes, a density evolution analysis enables joint optimization of both outer and inner code parameters for maximum throughput. With algebraic codes, we invoke a similar analysis by approximating their average erasure correcting capability while assuming a large number of active transmitters. The proposed low-complexity schemes operate at a significantly smaller gap to capacity than the state of the art. Our schemes apply both to a multiple access scenario where the number of users within a frame is known a priori, and to a random access scenario where that number is known only to the decoder. In the latter case, we optimize an outage probability due to the variability in user activity
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