Suppressing Fractional Pseudocodewords by Eliminating Small Instantons

Junjun GUO  Jianjun MU  Xiaopeng JIAO  Peng ZHAO  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E99-A   No.2   pp.674-677
Publication Date: 2016/02/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E99.A.674
Type of Manuscript: LETTER
Category: Coding Theory
LDPC codes,  pseudocodewords,  instantons,  fractional distance,  linear programming (LP) decoding,  

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In this letter, a new method is presented to suppress fractional pseudocodewords by eliminating small instantons of irregular low-density parity-check (LDPC) codes under the linear programming (LP) decoding over the binary symmetric channel (BSC). By appending several new rows found by the integer linear programming formulation to the original parity-check matrix, the optimal distribution spectrum of BSC-instantons in the modified code is obtained. Simulation results show that the proposed method can improve the fractional distance of parity-check matrices and considerably enhance the error-correcting performance of irregular LDPC codes under the LP decoding at the cost of a slightly loss of the original code rate.