4,360 research outputs found
Analysis and Design of Tuned Turbo Codes
It has been widely observed that there exists a fundamental trade-off between
the minimum (Hamming) distance properties and the iterative decoding
convergence behavior of turbo-like codes. While capacity achieving code
ensembles typically are asymptotically bad in the sense that their minimum
distance does not grow linearly with block length, and they therefore exhibit
an error floor at moderate-to-high signal to noise ratios, asymptotically good
codes usually converge further away from channel capacity. In this paper, we
introduce the concept of tuned turbo codes, a family of asymptotically good
hybrid concatenated code ensembles, where asymptotic minimum distance growth
rates, convergence thresholds, and code rates can be traded-off using two
tuning parameters, {\lambda} and {\mu}. By decreasing {\lambda}, the asymptotic
minimum distance growth rate is reduced in exchange for improved iterative
decoding convergence behavior, while increasing {\lambda} raises the asymptotic
minimum distance growth rate at the expense of worse convergence behavior, and
thus the code performance can be tuned to fit the desired application. By
decreasing {\mu}, a similar tuning behavior can be achieved for higher rate
code ensembles.Comment: Accepted for publication in IEEE Transactions on Information Theor
Fault-Tolerance of "Bad" Quantum Low-Density Parity Check Codes
We discuss error-correction properties for families of quantum low-density
parity check (LDPC) codes with relative distance that tends to zero in the
limit of large blocklength. In particular, we show that any family of LDPC
codes, quantum or classical, where distance scales as a positive power of the
block length, , , can correct all errors with
certainty if the error rate per (qu)bit is sufficiently small. We specifically
analyze the case of LDPC version of the quantum hypergraph-product codes
recently suggested by Tillich and Z\'emor. These codes are a finite-rate
generalization of the toric codes, and, for sufficiently large quantum
computers, offer an advantage over the toric codes.Comment: 4.5 pages, 1 figur
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