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What is Binary symmetric channel?

A channel model in which 0 or 1 is sent and each bit flips with the same probability p regardless of the value sent, independently of the other bits. Also called a BSC. Its channel capacity is C = 1 − H(p) bits per use (H(p) = −p log₂ p − (1 − p) log₂(1 − p)): about 0.53 bits for p = 0.1 and 0 for p = 0.5. At p = 1 every bit flips, so inverting the received value recovers the data without error, and the capacity returns to 1. It is the basic model for studying the performance of error-correcting codes for bit errors.

Japanese name: 二元対称通信路

Binary symmetric channel appears in 1 practice question across 1 topic, including Information Theory and Coding Basics.

Field: Information Theory and Coding Basics

Try it: questions about Binary symmetric channel

In a binary symmetric channel, 0s and 1s are sent and each bit flips independently with probability 0.1. With the binary entropy function H(p) = −p log₂ p − (1 − p) log₂(1 − p), H(0.1) ≈ 0.469. Which of the following is closest to the channel capacity of this channel per transmission?

  1. AAbout 0.47 bits
  2. BAbout 0.53 bits
  3. C0.9 bits
Show answer and explanation

Answer: B. About 0.53 bits

The channel capacity of a binary symmetric channel is C = 1 − H(p), the value of the mutual information when 0 and 1 are sent with equal probability. For p = 0.1, C ≈ 1 − 0.469 = 0.531, about 0.53 bits per transmission. With suitable error-correcting codes, data can be sent at up to this rate with an arbitrarily small error rate. At p = 0.5, the received value is unrelated to the value sent, and the capacity is 0.

Binary symmetric channel in the explanations

Questions that mention Binary symmetric channel (1)

  1. In a binary symmetric channel, 0s and 1s are sent and each bit flips independently with probability 0.1. With the binary entropy function H(p) = −p log₂ p − (1 − p) log₂(1 − p), H(0.1) ≈ 0.469. Which of the following is closest to the channel capacity of this channel per transmission?

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Related terms

Information entropy Shannon–Hartley theorem Mutual information Average code length Forward error correction (FEC) Hamming code Hamming distance Huffman coding Kraft inequality Lossless compression

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