Capacity-achieving Polar-based LDGM Codes with Crowdsourcing Applications

01/31/2020

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by   James Chin-Jen Pang, et al.

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In this paper we study codes with sparse generator matrices. More specifically, codes with a certain constraint on the weight of all the columns in the generator matrix are considered. The end result is the following. For any binary-input memoryless symmetric (BMS) channel and any epsilon > 2 epsilon*, where epsilon^* = 1/6-5/3log4/3≈ 0.085, we show an explicit sequence of capacity-achieving codes with all the column wights of the generator matrix upper bounded by (log N)^1+epsilon, where N is the code block length. The constructions are based on polar codes. Applications to crowdsourcing are also shown.