21,761 research outputs found
Polarization-Adjusted Convolutional (PAC) Codes as a Concatenation of Inner Cyclic and Outer Polar- and Reed-Muller-like Codes
Polarization-adjusted convolutional (PAC) codes are a new family of linear
block codes that can perform close to the theoretical bounds in the short
block-length regime. These codes combine polar coding and convolutional coding.
In this study, we show that PAC codes are equivalent to a new class of codes
consisting of inner cyclic codes and outer polar- and Reed-Muller-like codes.
We leverage the properties of cyclic codes to establish that PAC codes
outperform polar- and Reed-Muller-like codes in terms of minimum distance
A Reduced Latency List Decoding Algorithm for Polar Codes
Long polar codes can achieve the capacity of arbitrary binary-input discrete
memoryless channels under a low complexity successive cancelation (SC) decoding
algorithm. But for polar codes with short and moderate code length, the
decoding performance of the SC decoding algorithm is inferior. The cyclic
redundancy check (CRC) aided successive cancelation list (SCL) decoding
algorithm has better error performance than the SC decoding algorithm for short
or moderate polar codes. However, the CRC aided SCL (CA-SCL) decoding algorithm
still suffer from long decoding latency. In this paper, a reduced latency list
decoding (RLLD) algorithm for polar codes is proposed. For the proposed RLLD
algorithm, all rate-0 nodes and part of rate-1 nodes are decoded instantly
without traversing the corresponding subtree. A list maximum-likelihood
decoding (LMLD) algorithm is proposed to decode the maximum likelihood (ML)
nodes and the remaining rate-1 nodes. Moreover, a simplified LMLD (SLMLD)
algorithm is also proposed to reduce the computational complexity of the LMLD
algorithm. Suppose a partial parallel list decoder architecture with list size
is used, for an (8192, 4096) polar code, the proposed RLLD algorithm can
reduce the number of decoding clock cycles and decoding latency by 6.97 and
6.77 times, respectively.Comment: 7 pages, accepted by 2014 IEEE International Workshop on Signal
Processing Systems (SiPS
Countably Infinite Multilevel Source Polarization for Non-Stationary Erasure Distributions
Polar transforms are central operations in the study of polar codes. This
paper examines polar transforms for non-stationary memoryless sources on
possibly infinite source alphabets. This is the first attempt of source
polarization analysis over infinite alphabets. The source alphabet is defined
to be a Polish group, and we handle the Ar{\i}kan-style two-by-two polar
transform based on the group. Defining erasure distributions based on the
normal subgroup structure, we give recursive formulas of the polar transform
for our proposed erasure distributions. As a result, the recursive formulas
lead to concrete examples of multilevel source polarization with countably
infinite levels when the group is locally cyclic. We derive this result via
elementary techniques in lattice theory.Comment: 12 pages, 1 figure, a short version has been accepted by the 2019
IEEE International Symposium on Information Theory (ISIT2019
On the Weight Spectrum Improvement of Pre-transformed Reed-Muller Codes and Polar Codes
Pre-transformation with an upper-triangular matrix (including cyclic
redundancy check (CRC), parity-check (PC) and polarization-adjusted
convolutional (PAC) codes) improves the weight spectrum of Reed-Muller (RM)
codes and polar codes significantly. However, a theoretical analysis to
quantify the improvement is missing. In this paper, we provide asymptotic
analysis on the number of low-weight codewords of the original and
pre-transformed RM codes respectively, and prove that pre-transformation
significantly reduces low-weight codewords, even in the order sense. For polar
codes, we prove that the average number of minimum-weight codewords does not
increase after pre-transformation. Both results confirm the advantages of
pre-transformation
Design, Performance, and Complexity of CRC-Aided List Decoding of Convolutional and Polar Codes for Short Messages
Motivated by the need to communicate short control messages in 5G and beyond,
this paper carefully designs codes for cyclic redundancy check (CRC)-aided list
decoding of tail-biting convolutional codes (TBCCs) and polar codes. Both codes
send a 32-bit message using an 11-bit CRC and 512 transmitted bits. We aim to
provide a careful, fair comparison of the error performance and decoding
complexity of polar and TBCC techniques for a specific case. Specifically, a
TBCC is designed to match the rate of a (512, 43) polar code, and optimal
11-bit CRCs for both codes are designed. The paper examines the distance
spectra of the polar and TBCC codes, illuminating the different distance
structures for the two code types. We consider both adaptive and non-adaptive
CRC-aided list decoding schemes. For polar codes, an adaptive decoder must
start with a larger list size to avoid an error floor. For rate-32/512 codes
with an 11-bit CRC, the optimized CRC-TBCC design achieves a lower total
failure rate than the optimized CRC-polar design. Simulations showed that the
optimized CRC-TBCC design achieved significantly higher throughput than the
optimized CRC-polar design, so that the TBCC solution achieved a lower total
failure rate while requiring less computational complexity.Comment: First revision submitted to IEEE Transactions on Communication
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