Recursive error correction for general Reed-Muller codes

نویسندگان

  • Ilya Dumer
  • Kirill Shabunov
چکیده

Reed-Muller (RM) codes of growing length n and distance d are considered over a binary symmetric channel. A recursive decoding algorithm is designed that has complexity of order n log n and corrects most error patterns of weight (d ln d)/2. The presented algorithm outperforms other algorithms with nonexponential decoding complexity, which are known for RM codes. We evaluate code performance using a new probabilistic technique that disintegrates decoding into a sequence of recursive steps. This allows us to define the most error-prone information symbols and find the highest transition error probability p, which yields a vanishing output error probability on long codes.

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

Recursive List Decoding for Reed-Muller Codes

We consider recursive decoding for Reed-Muller (RM) codes and their subcodes. Two new recursive techniques are described. We analyze asymptotic properties of these algorithms and show that they substantially outperform other decoding algorithms with nonexponential complexity known for RM codes. Decoding performance is further enhanced by using intermediate code lists and permutation procedures....

متن کامل

Reed-Muller Codes for Peak Power Control in Multicarrier CDMA

Reed-Muller codes are studied for peak power control in multicarrier code-division multiple access (MC-CDMA) communication systems. In a coded MC-CDMA system, the information data multiplexed from users is encoded by a Reed-Muller subcode and the codeword is fully-loaded to Walsh-Hadamard spreading sequences. The polynomial representation of a coded MC-CDMA signal is established for theoretical...

متن کامل

On bit-level trellis complexity of Reed-Muller codes

A formula, which relates the state dimensions of a minimal trellis of a Reed-Muller code to those of another Reed-Muller code with lower order and shorter length, is derived in this correspondence. State dimension at every position of a minimal trellis of any Reed-Muller code can be obtained by a recursive application of this formula.

متن کامل

Polarization Codes: Characterization of Exponent, Bounds, and Constructions

Polarization codes were recently introduced by Arıkan. They achieve the capacity of arbitrary symmetric binaryinput discrete memoryless channels (and even extensions thereof) under a low complexity successive decoding strategy. The original polar code construction is closely related to the recursive construction of Reed-Muller codes and is based on the 2× 2 matrix

متن کامل

Reed-Muller Codec Simulation Performance

The approach to error correction coding taken by modern digital communication systems started in the late 1940’s with the ground breaking work of Shannon, Hamming and Golay. ReedMuller (RM) codes were an important step beyond the Hamming and Golay codes because they allowed more flexibility in the size of the code word and the number of correctable errors per code word. Whereas the Hamming and ...

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:
  • Discrete Applied Mathematics

دوره 154  شماره 

صفحات  -

تاریخ انتشار 2006