pixelization?

assuming this is in movie broadcasts, it may be inherent in the hd masters. backround objects like 'water', 'sand', 'window blinds', and much more, are extremely tuff to control.

I'm going to have to side with the compression crowd. Sometimes Comcast compresses the hell out of HD content on less popular channels to the point that I switch to the SD feed. This practice is more prevalent during prime time and weekends.

I sometimes see pixelization on my old CRT TV set, so it must be in the cable signal.

You should check into having the signal amplified by your cable company. It sounds like you have a weak signal.

This is a natural consequence of how video compression works.

The images are split up into 8x8 sample blocks which are converted into the frequency domain where you have an average level for the block plus the changes across the whole block, that occur twice, etc.

Periodically a full still frame is sent.

Subsequent frames are encoded with how far different groups of blocks have moved plus the changes.

When there's fast motion or camera pans there are more changes which must be represented and the system starts discarding the high frequencies and small color/intensity changes that make up details.

Cramming more channels into the same system like cable and satellite companies do reduces the bandwidth available to each one so more information needs to be thrown out.