Provably Efficient Instanton Search Algorithm for LP decoding of LDPC codes over the BSC

نویسندگان

  • Shashi Kiran Chilappagari
  • Michael Chertkov
چکیده

We consider Linear Programming (LP) decoding of a fixed Low-Density Parity-Check (LDPC) code over the Binary Symmetric Channel (BSC). The LP decoder fails when it outputs a pseudo-codeword which is not a codeword. We design an efficient algorithm termed the Instanton Search Algorithm (ISA) which, given a random input, generates a set of flips called the BSC-instanton. We prove that: (a) the LP decoder fails for any set of flips with support vector including an instanton; (b) for any input, the algorithm outputs an instanton in the number of steps upper-bounded by twice the number of flips in the input. Repeated sufficient number of times, the ISA outcomes the number of unique instantons of different sizes.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Search Based Weighted Multi-Bit Flipping Algorithm for High-Performance Low-Complexity Decoding of LDPC Codes

In this paper, two new hybrid algorithms are proposed for decoding Low Density Parity Check (LDPC) codes. Original version of the proposed algorithms named Search Based Weighted Multi Bit Flipping (SWMBF). The main idea of these algorithms is flipping variable multi bits in each iteration, change in which leads to the syndrome vector with least hamming weight. To achieve this, the proposed algo...

متن کامل

Finding Small Fundamental Instantons of LDPC Codes by Path Extension

SUMMARY In this letter, we present a new scheme to find small fundamental instantons (SFIs) of regular low-density parity-check (LDPC) codes for the linear programming (LP) decoding over the binary symmetric channel (BSC). Based on the fact that each instanton-induced graph (IIG) contains at least one short cycle, we determine potential instantons by constructing possible IIGs which contain sho...

متن کامل

Search Based Weighted Multi-Bit Flipping Algorithm for High-Performance Low-Complexity Decoding of LDPC Codes

In this paper, two new hybrid algorithms are proposed for decoding Low Density Parity Check (LDPC) codes. Original version of the proposed algorithms named Search Based Weighted Multi Bit Flipping (SWMBF). The main idea of these algorithms is flipping variable multi bits in each iteration, change in which leads to the syndrome vector with least hamming weight. To achieve this, the proposed algo...

متن کامل

Decoding Error-Correcting Codes via Linear Programming by

Error-correcting codes are fundamental tools used to transmit digital information over unreliable channels. Their study goes back to the work of Hamming [Ham50] and Shannon [Sha48], who used them as the basis for the field of information theory. The problem of decoding the original information up to the full error-correcting potential of the system is often very complex, especially for modern c...

متن کامل

Decoding error-correcting codes via linear programming

Error-correcting codes are fundamental tools used to transmit digital information over unreliable channels. Their study goes back to the work of Hamming [Ham50] and Shannon [Sha48], who used them as the basis for the field of information theory. The problem of decoding the original information up to the full error-correcting potential of the system is often very complex, especially for modern c...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • CoRR

دوره abs/0808.2515  شماره 

صفحات  -

تاریخ انتشار 2008