Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Parameterized Gallager's First Bounds for Binary Linear Codes over
  AWGN Channels   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.

25
The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
20
The categories of this paper are: acc-phys