Correct Introduction, round 1

letter.tex

@@ -102,7 +102,7 @@ attempted to be corrected.
 We suggesst an empirical rule with which the components most likely needing
 correction can be determined.
 Using this insight and performing a subsequent ``ML-in-the-list'' decoding,
-a gain of up to approximately 1 dB is achieved compared to conventional
+a gain of up to 1 dB is achieved compared to conventional
 proximal decoding, depending on the decoder parameters and the code.
 \end{abstract}
 
@@ -126,7 +126,7 @@ the reliability of data by detecting and correcting any errors that may occur
 during its transmission or storage.
 One class of binary linear codes, \textit{low-density parity-check} (LDPC)
 codes, has become especially popular due to its ability to reach arbitrarily
-small probabilities of error at code rates up to the capacity of the channel
+small error probabilities at code rates up to the capacity of the channel
 \cite{mackay99}, while retaining a structure that allows for very efficient
 decoding.
 While the established decoders for LDPC codes, such as belief propagation (BP)
@@ -139,37 +139,37 @@ Optimization based decoding algorithms are an entirely different way of
 approaching the decoding problem.
 A number of different such algorithms have been introduced.
 The field of \textit{linear programming} (LP) decoding \cite{feldman_paper},
-for example, represents one class of such algorithms, based on a reformulation
+for example, represents one class of such algorithms, based on a relaxation
 of the \textit{maximum likelihood} (ML) decoding problem as a linear program.
 Many different optimization algorithms can be used to solve the resulting
-problem \cite{interior_point_decoding, ADMM, adaptive_lp_decoding}.
+problem \cite{ADMM, adaptive_lp_decoding, interior_point_decoding}.
 Recently, proximal decoding for LDPC codes was presented by
-Wadayama et al. \cite{proximal_paper}.
-It is a novel approach and relies on a non-convex optimization formulation
+Wadayama \textit{et al.} \cite{proximal_paper}.
+Proximal decoding relies on a non-convex optimization formulation
 of the \textit{maximum a posteriori} (MAP) decoding problem.
 
 The aim of this work is to improve upon the performance of proximal decoding by
 first presenting an examination of the algorithm's behavior and then suggesting
 an approach to mitigate some of its flaws.
-This analysis is performed within the context of
+This analysis is performed for
 \textit{additive white Gaussian noise} (AWGN) channels.
-It is first observed that, while the algorithm initially moves the estimate in
-the right direction, in the final steps of the decoding process convergence to
-the correct codeword is often not achieved.
-Furthermore, it is suggested that the reason for this behavior is the nature
+We first observe that the algorithm initially moves the estimate in
+the right direction, however, in the final steps of the decoding process,
+convergence to the correct codeword is often not achieved.
+Furthermore, we suggest that the reason for this behavior is the nature
 of the decoding algorithm itself, comprising two separate gradient descent
 steps working adversarially.
 
-A method to mitigate this effect is proposed by appending an additional step
-to the decoding process.
+We propose a method mitigate this effect by appending an
+additional step to the decoding process.
 In this additional step, the components of the estimate with the highest
 probability of being erroneous are identified.
 New codewords are then generated, over which an ``ML-in-the-list''
 \cite{ml_in_the_list} decoding is performed.
 A process to conduct this identification is proposed in this paper.
 Using the improved algorithm, a gain of up to
-approximately 1 dB can be achieved compared to proximal decoding, depending on
-the parameters chosen and the code considered.
+1 dB can be achieved compared to conventional proximal decoding,
+depending on the decoder parameters and the code.
 
 
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