On Parameterized Gallager's First Bounds for Binary Linear Codes over AWGN Channels

Details On Parameterized Gallager's First Bounds for Binary Linear Codes over AWGN Channels On Parameterized Gallager's First Bounds for Binary Linear Codes over AWGN Channels

2012-02-03

arxiv.org/abs/1202.0592v3

Computer Science

Information Theory

Scientific paper

In this paper, nested Gallager regions with a single parameter is introduced to exploit Gallager's first bounding technique (GFBT). We present a necessary and sufficient condition on the optimal parameter. We also present a sufficient condition (with a simple geometrical explanation) under which the optimal parameter does not depend on the signal-to-noise ratio (SNR). With this general framework, three existing upper bounds are revisited, including the tangential bound (TB) of Berlekamp, the sphere bound (SB) of Herzberg and Poltyrev, and the tangential-sphere bound (TSB) of Poltyrev. This paper also reveals that the SB of Herzberg and Poltyrev is equivalent to the SB of Kasami et al., which was rarely cited in literature.

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