1,817 research outputs found
Long Nonbinary Codes Exceeding the Gilbert - Varshamov Bound for any Fixed Distance
Let A(q,n,d) denote the maximum size of a q-ary code of length n and distance
d. We study the minimum asymptotic redundancy \rho(q,n,d)=n-log_q A(q,n,d) as n
grows while q and d are fixed. For any d and q<=d-1, long algebraic codes are
designed that improve on the BCH codes and have the lowest asymptotic
redundancy \rho(q,n,d) <= ((d-3)+1/(d-2)) log_q n known to date. Prior to this
work, codes of fixed distance that asymptotically surpass BCH codes and the
Gilbert-Varshamov bound were designed only for distances 4,5 and 6.Comment: Submitted to IEEE Trans. on Info. Theor
Improved linear programming decoding of LDPC codes and bounds on the minimum and fractional distance
We examine LDPC codes decoded using linear programming (LP). Four
contributions to the LP framework are presented. First, a new method of
tightening the LP relaxation, and thus improving the LP decoder, is proposed.
Second, we present an algorithm which calculates a lower bound on the minimum
distance of a specific code. This algorithm exhibits complexity which scales
quadratically with the block length. Third, we propose a method to obtain a
tight lower bound on the fractional distance, also with quadratic complexity,
and thus less than previously-existing methods. Finally, we show how the
fundamental LP polytope for generalized LDPC codes and nonbinary LDPC codes can
be obtained.Comment: 17 pages, 8 figures, Submitted to IEEE Transactions on Information
Theor
On a Class of Optimal Nonbinary Linear Unequal-Error-Protection Codes for Two Sets of Messages
Several authors have addressed the problem of designing good linear unequal error protection (LUEP) codes. However, very little is known about good nonbinary LUEP codes. We present a class of optimal nonbinary LUEP codes for two different sets of messages. By combining t-error-correcting ReedSolomon (RS) codes and shortened nonbinary Hamming codes, we obtain nonbinary LUEP codes that protect one set of messages against any t or fewer symbol errors and the remaining set of messages against any single symbol error. For t ≥ 2, we show that these codes are optimal in the sense of achieving the Hamming lower bound on the number of redundant symbols of a nonbinary LUEP code with the same parameters
Performance Prediction of Nonbinary Forward Error Correction in Optical Transmission Experiments
In this paper, we compare different metrics to predict the error rate of
optical systems based on nonbinary forward error correction (FEC). It is shown
that the correct metric to predict the performance of coded modulation based on
nonbinary FEC is the mutual information. The accuracy of the prediction is
verified in a detailed example with multiple constellation formats, FEC
overheads in both simulations and optical transmission experiments over a
recirculating loop. It is shown that the employed FEC codes must be universal
if performance prediction based on thresholds is used. A tutorial introduction
into the computation of the threshold from optical transmission measurements is
also given.Comment: submitted to IEEE/OSA Journal of Lightwave Technolog
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