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Convolutional codes. Tomashevich Victor. Introduction. Convolutional codes map information to code bits sequentially by convolving a sequence of information bits with “generator” sequences A convolutional encoder encodes K information bits to N>K code bits at one time step

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convolutional codes

Convolutional codes

Tomashevich Victor

introduction
Introduction
  • Convolutional codes map information to code bits sequentially by convolving a sequence of information bits with “generator” sequences
  • A convolutional encoder encodes K information bits to N>K code bits at one time step
  • Convolutional codes can be regarded as block codes for which the encoder has a certain structure such that we can express the encoding operation as convolution
slide5
The convolutional code is linear
  • The encoding mapping is bijective
  • Code bits generated at time step i are affected by information bits up to M time steps i – 1, i – 2, …, i – M back in time. M is the maximal delay of information bits in the encoder
  • Code memory is the (minimal) number of registers to construct an encoding circuit for the code.
  • Constraint length is the overall number of information bits affecting code bits generated at time step i: =code memory + K=MK + K=(M + 1)K
  • A convolutional code is systematic if the N code bits generated at time step i contain the K information bits