Low-precision A/D conversion for maximum information rate in channels with memory

Georg Zeitler, Andrew C. Singer, Gerhard Kramer

Research output: Contribution to journalArticlepeer-review


Analog-to-digital converters that maximize the information rate between the quantized channel output sequence and the channel input sequence are designed for discrete-time channels with intersymbol-interference, additive noise, and for independent and identically distributed signaling. Optimized scalar quantizers with Λ regions achieve the full information rate of log-2(Λ) bits per channel use with a transmit alphabet of size Λ at infinite signal-to-noise ratio; these quantizers, however, are not necessarily uniform quantizers. Low-precision scalar and two-dimensional analog-to-digital converters are designed at finite signal-to-noise ratio, and an upper bound on the information rate is derived. Simulation results demonstrate the effectiveness of the designed quantizers over conventional quantizers. The advantage of the new quantizers is further emphasized by an example of a channel for which a slicer (with a single threshold at zero) and a carefully optimized channel input with memory fail to achieve a rate of one bit per channel use at high signal-to-noise ratio, in contrast to memoryless binary signaling and an optimized quantizer.

Original languageEnglish (US)
Article number6242364
Pages (from-to)2511-2521
Number of pages11
JournalIEEE Transactions on Communications
Issue number9
StatePublished - 2012


  • Analog-digital conversion
  • intersymbol interference
  • quantization

ASJC Scopus subject areas

  • Electrical and Electronic Engineering


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