Core Concepts
The asymptotic error rates of LDPC and polar codes are functions of complexity T and code length N, in the form of 2^(-a2^b T/N), where a and b are constants that depend on channel and coding schemes. Polar codes asymptotically outperform (J, K)-regular LDPC codes with a code rate R ≤1 - J(J-1)/(2J+(J-1)) in the low-complexity regime (T ≤O(NlogN)).
Abstract
The paper explores the performance-complexity tradeoff of low-complexity decoders for LDPC and polar codes.
For LDPC codes:
Establishes a lower bound on the BER as a function of decoding complexity, showing a double-exponential reduction in error rate with the number of iterations.
Analyzes the average BER over the ensemble of LDPC codes, providing a tighter lower bound.
For (J, K)-regular LDPC codes, shows the BER and BLER are bounded by Ω(2^(-c1c2^(log2(J-1)(K-1)/(2J))T/N)).
For polar codes:
Characterizes the tradeoff between the complexity of the polar code SSC decoder and its BLER.
Shows the BLER is upper bounded by O(2^(-0.5T/N)) for complexity T ∈(2NloglogN, NlogN).
Demonstrates that polar codes asymptotically outperform (J, K)-regular LDPC codes with R ≤1 - J(J-1)/(2J+(J-1)) in the low-complexity regime.
The results indicate that to further enhance the decoding efficiency for LDPC codes, the key lies in how to efficiently pass messages on the factor graph. Polar codes exhibit superior decoding efficiency in the low-complexity regime due to their ability to effectively gather and utilize information.
Stats
The number of messages passed (NMP) is used as the complexity measure T.