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arXiv · 1705.06847

Syndrome-Coupled Rate-Compatible Error-Correcting Codes

Pengfei Huang·Yi Liu·Xiaojie Zhang·Paul H. Siegel·Erich F. Haratsch
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Abstract

Rate-compatible error-correcting codes (ECCs), which consist of a set of extended codes, are of practical interest in both wireless communications and data storage. In this work, we first study the lower bounds for rate-compatible ECCs, thus proving the existence of good rate-compatible codes. Then, we propose a general framework for constructing rate-compatible ECCs based on cosets and syndromes of a set of nested linear codes. We evaluate our construction from two points of view. From a combinatorial perspective, we show that we can construct rate-compatible codes with increasing minimum distances. From a probabilistic point of view, we prove that we are able to construct capacity-achieving rate-compatible codes.

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Pengfei Huang, Yi Liu, Xiaojie Zhang, Paul H. Siegel, Erich F. Haratsch. 2017-05-19. Syndrome-Coupled Rate-Compatible Error-Correcting Codes. https://arxiv.org/abs/1705.06847

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