Gallager codes with large block length and low rate ({\it e.g.}, N \simeq 10,000-40,000, R \simeq 0.25-0.5) have been shown to have record-breaking performance for low signal-to-noise applications. Gallager codes with high rates (R \simeq 0.8-0.94) are also excellent, outperforming comparable BCH and Reed-Solomon codes, even at short blocklength (N \simeq 2,000-4,000). This paper looks in more detail at high-rate Gallager codes, addressing the following issues. First, we recap the performance improvement obtained by switching from a Reed-Solomon code to a comparable Gallager code. Second, we investigate the benefit of increasing the blocklength of the Gallager code, and investigate the variability in performance among randomly-created codes. Third, we show the benefit of reducing the rate of the code, \ie, increasing its redundancy. Fourth, we describe modifications to the code that are appropriate if there are many parallel channels that contaminate each other with crosstalk, as might be the case in an optical channel, and quantify the benefits of these changes.
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